Building Functions - Common Core: High School - Functions

Card 0 of 432

Question

Which graph represents the the inverse of the following function?

Answer

This question is testing ones ability to recognize and construct a function's inverse from its graph.

For the purpose of Common Core Standards, "Read values of an inverse function from a graph or a table, given that the function has an inverse." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4c). It is important to note that this standard is not directly tested on but is used for building a deeper understanding on inverses and their functions.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what it means to be an inverse.

An inverse function is found algebraically as follows.

$y=x+c\Rightarrow x=y+c$

Now solve for the variable in the new (inverse) function.

$\x=y+c \x-c=y \y^{-1}=x-c$

Graphically, the inverse is the mirror image reflected over the line of symmetry. In other words, the coordinate pair components are switched.

Step 2: Construct coordinate pairs of the given graph.

Looking at the graph above, the following table of coordinate pairs can be constructed.

$\begin{tabular}{ |c|c| } \hline x & y \ \hline -4 & 0 \ -3&1\ -2&2\ -1&3\ 0& 4 \ 4&8\ \hline \end{tabular}$

Step 3: Swap the points with the points to create the coordinate pairs of the inverse graph.

$\begin{tabular}{ |c|c| } \hline x & y \ \hline 0&-4 \ 1&-3\ 2&-2\ 3&-1\4&0 \ 8&4\ \hline \end{tabular}$

Step 4: Graph the inverse function.

Compare your answer with the correct one above

Question

Which graph represents the the inverse of the following function?

Answer

This question is testing ones ability to recognize and construct a function's inverse from its graph.

For the purpose of Common Core Standards, "Read values of an inverse function from a graph or a table, given that the function has an inverse." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4c). It is important to note that this standard is not directly tested on but is used for building a deeper understanding on inverses and their functions.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what it means to be an inverse.

An inverse function is found algebraically as follows.

$y=x+c\Rightarrow x=y+c$

Now solve for the variable in the new (inverse) function.

$\x=y+c \x-c=y \y^{-1}=x-c$

Graphically, the inverse is the mirror image reflected over the line of symmetry. In other words, the coordinate pair components are switched.

Step 2: Construct coordinate pairs of the given graph.

Looking at the graph above, the following table of coordinate pairs can be constructed.

$\begin{tabular}{ |c|c| } \hline x & y \ \hline 0 & -2 \ 1&-1\ 2&0\ 3&1\ 4& 2 \ 5&3\ \hline \end{tabular}$

Step 3: Swap the points with the points to create the coordinate pairs of the inverse graph.

$\begin{tabular}{ |c|c| } \hline x & y \ \hline -2&0 \ -1&1\ 0&2\ 1&3\2&4 \ 3&5\ \hline \end{tabular}$

Step 4: Graph the inverse function.

Compare your answer with the correct one above

Question

Which graph represents the the inverse of the following function?

Answer

This question is testing ones ability to recognize and construct a function's inverse from its graph.

For the purpose of Common Core Standards, "Read values of an inverse function from a graph or a table, given that the function has an inverse." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4c). It is important to note that this standard is not directly tested on but is used for building a deeper understanding on inverses and their functions.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what it means to be an inverse.

An inverse function is found algebraically as follows.

$y=x+c\Rightarrow x=y+c$

Now solve for the variable in the new (inverse) function.

$\x=y+c \x-c=y \y^{-1}=x-c$

Graphically, the inverse is the mirror image reflected over the line of symmetry. In other words, the coordinate pair components are switched.

Step 2: Construct coordinate pairs of the given graph.

Looking at the graph above, the following table of coordinate pairs can be constructed.

$\begin{tabular}{ |c|c| } \hline x & y \ \hline -2&0 \ -1&1\ 0&2\ 1&3\2&4 \ 3&5\ \hline \end{tabular}$

Step 3: Swap the points with the points to create the coordinate pairs of the inverse graph.

$\begin{tabular}{ |c|c| } \hline x & y \ \hline 0 & -2 \ 1&-1\ 2&0\ 3&1\ 4& 2 \ 5&3\ \hline \end{tabular}$

Step 4: Graph the inverse function.

Compare your answer with the correct one above

Question

Which graph represents the the inverse of the following function?

Answer

This question is testing ones ability to recognize and construct a function's inverse from its graph.

For the purpose of Common Core Standards, "Read values of an inverse function from a graph or a table, given that the function has an inverse." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4c). It is important to note that this standard is not directly tested on but is used for building a deeper understanding on inverses and their functions.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what it means to be an inverse.

An inverse function is found algebraically as follows.

$y=x+c\Rightarrow x=y+c$

Now solve for the variable in the new (inverse) function.

$\x=y+c \x-c=y \y^{-1}=x-c$

Graphically, the inverse is the mirror image reflected over the line of symmetry. In other words, the coordinate pair components are switched.

Step 2: Construct coordinate pairs of the given graph.

Looking at the graph above, the following table of coordinate pairs can be constructed.

$\begin{tabular}{ |c|c| } \hline x & y \ \hline 0 & 0 \ 1&3\ 2&6\ 3&9\ \hline \end{tabular}$

Step 3: Swap the points with the points to create the coordinate pairs of the inverse graph.

$\begin{tabular}{ |c|c| } \hline x & y \ \hline 0&0 \ 3&1\ 6&2\ 9&3\ \hline \end{tabular}$

Step 4: Graph the inverse function.

Compare your answer with the correct one above

Question

Which graph represents the the inverse of the following function?

Answer

This question is testing ones ability to recognize and construct a function's inverse from its graph.

For the purpose of Common Core Standards, "Read values of an inverse function from a graph or a table, given that the function has an inverse." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4c). It is important to note that this standard is not directly tested on but is used for building a deeper understanding on inverses and their functions.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what it means to be an inverse.

An inverse function is found algebraically as follows.

$y=x+c\Rightarrow x=y+c$

Now solve for the variable in the new (inverse) function.

$\x=y+c \x-c=y \y^{-1}=x-c$

Graphically, the inverse is the mirror image reflected over the line of symmetry. In other words, the coordinate pair components are switched.

Step 2: Construct coordinate pairs of the given graph.

Looking at the graph above, the following table of coordinate pairs can be constructed.

$\begin{tabular}{ |c|c| } \hline x & y \ \hline 0 & 0 \ 3&1\ 6&2\ 9&3\ \hline \end{tabular}$

Step 3: Swap the points with the points to create the coordinate pairs of the inverse graph.

$\begin{tabular}{ |c|c| } \hline x & y \ \hline 0&0 \ 1&3\ 2&6\ 3&9\ \hline \end{tabular}$

Step 4: Graph the inverse function.

Compare your answer with the correct one above

Question

Which graph represents the the inverse of the following function?

Answer

This question is testing ones ability to recognize and construct a function's inverse from its graph.

For the purpose of Common Core Standards, "Read values of an inverse function from a graph or a table, given that the function has an inverse." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4c). It is important to note that this standard is not directly tested on but is used for building a deeper understanding on inverses and their functions.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what it means to be an inverse.

An inverse function is found algebraically as follows.

$y=x+c\Rightarrow x=y+c$

Now solve for the variable in the new (inverse) function.

$\x=y+c \x-c=y \y^{-1}=x-c$

Graphically, the inverse is the mirror image reflected over the line of symmetry. In other words, the coordinate pair components are switched.

Step 2: Construct coordinate pairs of the given graph.

Looking at the graph above, the following table of coordinate pairs can be constructed.

$\begin{tabular}{ |c|c| } \hline x & y \ \hline 0 & -4 \ 1&-3\ 2&-2\ 3&-1\ 4& 0 \ 5&1\ \hline \end{tabular}$

Step 3: Swap the points with the points to create the coordinate pairs of the inverse graph.

$\begin{tabular}{ |c|c| } \hline x & y \ \hline -4&0 \ -3&1\ -2&2\ -1&3\0&4 \ 1&5\ \hline \end{tabular}$

Step 4: Graph the inverse function.

Compare your answer with the correct one above

Question

Which graph represents the the inverse of the following function?

Answer

This question is testing ones ability to recognize and construct a function's inverse from its graph.

For the purpose of Common Core Standards, "Read values of an inverse function from a graph or a table, given that the function has an inverse." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4c). It is important to note that this standard is not directly tested on but is used for building a deeper understanding on inverses and their functions.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what it means to be an inverse.

An inverse function is found algebraically as follows.

$y=x+c\Rightarrow x=y+c$

Now solve for the variable in the new (inverse) function.

$\x=y+c \x-c=y \y^{-1}=x-c$

Graphically, the inverse is the mirror image reflected over the line of symmetry. In other words, the coordinate pair components are switched.

Step 2: Construct coordinate pairs of the given graph.

Looking at the graph above, the following table of coordinate pairs can be constructed.

$\begin{tabular}{ |c|c| } \hline x & y \ \hline -4 & 0 \ -3&1\ -2&2\ -1&3\ 0& 4 \ 1&5\ \hline \end{tabular}$

Step 3: Swap the points with the points to create the coordinate pairs of the inverse graph.

$\begin{tabular}{ |c|c| } \hline x & y \ \hline 0&-4 \ 1&-3\ 2&-2\ 3&-1\4&0 \ 5&1\ \hline \end{tabular}$

Step 4: Graph the inverse function.

Compare your answer with the correct one above

Question

Which graph represents the the inverse of the following function?

Answer

This question is testing ones ability to recognize and construct a function's inverse from its graph.

For the purpose of Common Core Standards, "Read values of an inverse function from a graph or a table, given that the function has an inverse." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4c). It is important to note that this standard is not directly tested on but is used for building a deeper understanding on inverses and their functions.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what it means to be an inverse.

An inverse function is found algebraically as follows.

$y=x+c\Rightarrow x=y+c$

Now solve for the variable in the new (inverse) function.

$\x=y+c \x-c=y \y^{-1}=x-c$

Graphically, the inverse is the mirror image reflected over the line of symmetry. In other words, the coordinate pair components are switched.

Step 2: Construct coordinate pairs of the given graph.

Looking at the graph above, the following table of coordinate pairs can be constructed.

$\begin{tabular}{ |c|c| } \hline x & y \ \hline 0 & 0 \ 1&4\ 2&8\ \hline \end{tabular}$

Step 3: Swap the points with the points to create the coordinate pairs of the inverse graph.

$\begin{tabular}{ |c|c| } \hline x & y \ \hline 0&0 \ 4&1\ 8&2\ \hline \end{tabular}$

Step 4: Graph the inverse function.

Compare your answer with the correct one above

Question

Which graph represents the the inverse of the following function?

Answer

This question is testing ones ability to recognize and construct a function's inverse from its graph.

For the purpose of Common Core Standards, "Read values of an inverse function from a graph or a table, given that the function has an inverse." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4c). It is important to note that this standard is not directly tested on but is used for building a deeper understanding on inverses and their functions.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what it means to be an inverse.

An inverse function is found algebraically as follows.

$y=x+c\Rightarrow x=y+c$

Now solve for the variable in the new (inverse) function.

$\x=y+c \x-c=y \y^{-1}=x-c$

Graphically, the inverse is the mirror image reflected over the line of symmetry. In other words, the coordinate pair components are switched.

Step 2: Construct coordinate pairs of the given graph.

Looking at the graph above, the following table of coordinate pairs can be constructed.

$\begin{tabular}{ |c|c| } \hline x & y \ \hline 0 & 0 \ 4&1\ 8&2\ \hline \end{tabular}$

Step 3: Swap the points with the points to create the coordinate pairs of the inverse graph.

$\begin{tabular}{ |c|c| } \hline x & y \ \hline 0&0 \ 1&4\ 2&8\ \hline \end{tabular}$

Step 4: Graph the inverse function.

Compare your answer with the correct one above

Question

Which graph represents the the inverse of the following function?

Answer

This question is testing ones ability to recognize and construct a function's inverse from its graph.

For the purpose of Common Core Standards, "Read values of an inverse function from a graph or a table, given that the function has an inverse." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4c). It is important to note that this standard is not directly tested on but is used for building a deeper understanding on inverses and their functions.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what it means to be an inverse.

An inverse function is found algebraically as follows.

$y=x+c\Rightarrow x=y+c$

Now solve for the variable in the new (inverse) function.

$\x=y+c \x-c=y \y^{-1}=x-c$

Graphically, the inverse is the mirror image reflected over the line of symmetry. In other words, the coordinate pair components are switched.

Step 2: Construct coordinate pairs of the given graph.

Looking at the graph above, the following table of coordinate pairs can be constructed.

$\begin{tabular}{ |c|c| } \hline x & y \ \hline 0 & 0 \ 1&2\ 2&4\ 3&6\ 4& 8 \ \hline \end{tabular}$

Step 3: Swap the points with the points to create the coordinate pairs of the inverse graph.

$\begin{tabular}{ |c|c| } \hline x & y \ \hline 0&0 \ 2&1\ 4&2\ 6&3\8&4 \ \hline \end{tabular}$

Step 4: Graph the inverse function.

Compare your answer with the correct one above

Question

Which graph represents the the inverse of the following function?

Answer

This question is testing ones ability to recognize and construct a function's inverse from its graph.

For the purpose of Common Core Standards, "Read values of an inverse function from a graph or a table, given that the function has an inverse." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4c). It is important to note that this standard is not directly tested on but is used for building a deeper understanding on inverses and their functions.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what it means to be an inverse.

An inverse function is found algebraically as follows.

$y=x+c\Rightarrow x=y+c$

Now solve for the variable in the new (inverse) function.

$\x=y+c \x-c=y \y^{-1}=x-c$

Graphically, the inverse is the mirror image reflected over the line of symmetry. In other words, the coordinate pair components are switched.

Step 2: Construct coordinate pairs of the given graph.

Looking at the graph above, the following table of coordinate pairs can be constructed.

$\begin{tabular}{ |c|c| } \hline x & y \ \hline 0 & 0 \ 2&1\ 4&2\ 6&3\ 8& 4 \ \hline \end{tabular}$

Step 3: Swap the points with the points to create the coordinate pairs of the inverse graph.

$\begin{tabular}{ |c|c| } \hline x & y \ \hline 0&0 \ 1&2\ 2&4\ 3&6\4&8 \ \hline \end{tabular}$

Step 4: Graph the inverse function.

Compare your answer with the correct one above

Question

Which graph represents the the inverse of the following function?

Answer

This question is testing ones ability to recognize and construct a function's inverse from its graph.

For the purpose of Common Core Standards, "Read values of an inverse function from a graph or a table, given that the function has an inverse." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4c). It is important to note that this standard is not directly tested on but is used for building a deeper understanding on inverses and their functions.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what it means to be an inverse.

An inverse function is found algebraically as follows.

$y=x+c\Rightarrow x=y+c$

Now solve for the variable in the new (inverse) function.

$\x=y+c \x-c=y \y^{-1}=x-c$

Graphically, the inverse is the mirror image reflected over the line of symmetry. In other words, the coordinate pair components are switched.

Step 2: Construct coordinate pairs of the given graph.

Looking at the graph above, the following table of coordinate pairs can be constructed.

$\begin{tabular}{ |c|c| } \hline x & y \ \hline 0 & 6 \ 1&5\ 2&4\ 3&3\ 4&2 \ 5&1\ \hline \end{tabular}$

Step 3: Swap the points with the points to create the coordinate pairs of the inverse graph.

$\begin{tabular}{ |c|c| } \hline x & y \ \hline 6&0 \ 5&1\ 4&2\ 3&3\2&4 \ 1&5\ \hline \end{tabular}$

Step 4: Graph the inverse function.

Compare your answer with the correct one above

Question

There is an adjustable, cylindrical container in the science lab that is attached to a timer. The container holds a certain gas and the pressure of the gas in the container can be modeled by the function,

$P(s)=\frac{1}{2}+16s$

where is the size of the container.

Every minute the timer adjusts the size of the container and is modeled by the function,

where is in minutes.

Find an explicit expression that illustrates the amount of pressure of the gas in the container related to the time in minutes.

Answer

This question is testing one's ability to compose functions that are modeled by real world situations. Questions like these require in-depth critical reasoning skills and the ability to identify the meaning of composition of functions as they relate to scenarios.

For the purpose of Common Core Standards, composed functions falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A). Questions in this cluster depend heavily of building an understanding between real life situations as seen through a mathematical perspective.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what the question is asking for.

Step 2: Identify what is given/known from the question.

Step 3: Using algebraic methods creating function to describe relationship.

Step 4: Answer the question.

Following the steps listed above for this particular problem is as follows.

Step 1: Identify what the question is asking for.

The question is asking to find the composition of the two functions.

In other words, find .

Step 2: Identify what is given/known from the question.

The two functions are given in mathematical form.

$P(s)=\frac{1}{2}+16s$

Step 3: Using algebraic methods creating function to describe relationship.

To solve this problem, replace every in the pressure function with the entire function .

$\P(S(t))=\frac{1}{2}+16(10-2t) \ \P(S(t))=\frac{1}{2}+160-32t \ \P(S(t))=160.5-32t$

Step 4: Answer the question.

The explicit expression that illustrates the amount of pressure of the gas in the container related to the time in minutes is,

Compare your answer with the correct one above

Question

There is an adjustable, cylindrical container in the science lab that is attached to a timer. The container holds a certain gas and the pressure of the gas in the container can be modeled by the function,

$P(s)=\frac{1}{2}+14s$

where is the size of the container.

Every minute the timer adjusts the size of the container and is modeled by the function,

where is in minutes.

Find an explicit expression that illustrates the amount of pressure of the gas in the container related to the time in minutes.

Answer

This question is testing one's ability to compose functions that are modeled by real world situations. Questions like these require in-depth critical reasoning skills and the ability to identify the meaning of composition of functions as they relate to scenarios.

For the purpose of Common Core Standards, composed functions falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A). Questions in this cluster depend heavily of building an understanding between real life situations as seen through a mathematical perspective.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what the question is asking for.

Step 2: Identify what is given/known from the question.

Step 3: Using algebraic methods creating function to describe relationship.

Step 4: Answer the question.

Following the steps listed above for this particular problem is as follows.

Step 1: Identify what the question is asking for.

The question is asking to find the composition of the two functions.

In other words, find .

Step 2: Identify what is given/known from the question.

The two functions are given in mathematical form.

$P(s)=\frac{1}{2}+14s$

Step 3: Using algebraic methods creating function to describe relationship.

To solve this problem, replace every in the pressure function with the entire function .

$\P(S(t))=\frac{1}{2}+14(8-2t) \ \P(S(t))=\frac{1}{2}+112-28t \ \P(S(t))=112.5-28t$

Step 4: Answer the question.

The explicit expression that illustrates the amount of pressure of the gas in the container related to the time in minutes is,

Compare your answer with the correct one above

Question

There is an adjustable, cylindrical container in the science lab that is attached to a timer. The container holds a certain gas and the pressure of the gas in the container can be modeled by the function,

$P(s)=\frac{1}{2}+10s$

where is the size of the container.

Every minute the timer adjusts the size of the container and is modeled by the function,

where is in minutes.

Find an explicit expression that illustrates the amount of pressure of the gas in the container related to the time in minutes.

Answer

This question is testing one's ability to compose functions that are modeled by real world situations. Questions like these require in-depth critical reasoning skills and the ability to identify the meaning of composition of functions as they relate to scenarios.

For the purpose of Common Core Standards, composed functions falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A). Questions in this cluster depend heavily of building an understanding between real life situations as seen through a mathematical perspective.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what the question is asking for.

Step 2: Identify what is given/known from the question.

Step 3: Using algebraic methods creating function to describe relationship.

Step 4: Answer the question.

Following the steps listed above for this particular problem is as follows.

Step 1: Identify what the question is asking for.

The question is asking to find the composition of the two functions.

In other words, find .

Step 2: Identify what is given/known from the question.

The two functions are given in mathematical form.

$P(s)=\frac{1}{2}+10s$

Step 3: Using algebraic methods creating function to describe relationship.

To solve this problem, replace every in the pressure function with the entire function .

$\P(S(t))=\frac{1}{2}+10(10-2t) \ \P(S(t))=\frac{1}{2}+100-20t \ \P(S(t))=100.5-20t$

Step 4: Answer the question.

The explicit expression that illustrates the amount of pressure of the gas in the container related to the time in minutes is,

Compare your answer with the correct one above

Question

There is an adjustable, cylindrical container in the science lab that is attached to a timer. The container holds a certain gas and the pressure of the gas in the container can be modeled by the function,

$P(s)=\frac{1}{2}+6s$

where is the size of the container.

Every minute the timer adjusts the size of the container and is modeled by the function,

where is in minutes.

Find an explicit expression that illustrates the amount of pressure of the gas in the container related to the time in minutes.

Answer

This question is testing one's ability to compose functions that are modeled by real world situations. Questions like these require in-depth critical reasoning skills and the ability to identify the meaning of composition of functions as they relate to scenarios.

For the purpose of Common Core Standards, composed functions falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A). Questions in this cluster depend heavily of building an understanding between real life situations as seen through a mathematical perspective.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what the question is asking for.

Step 2: Identify what is given/known from the question.

Step 3: Using algebraic methods creating function to describe relationship.

Step 4: Answer the question.

Following the steps listed above for this particular problem is as follows.

Step 1: Identify what the question is asking for.

The question is asking to find the composition of the two functions.

In other words, find .

Step 2: Identify what is given/known from the question.

The two functions are given in mathematical form.

$P(s)=\frac{1}{2}+6s$

Step 3: Using algebraic methods creating function to describe relationship.

To solve this problem, replace every in the pressure function with the entire function .

$\P(S(t))=\frac{1}{2}+6(10-2t) \ \P(S(t))=\frac{1}{2}+60-12t \ \P(S(t))=60.5-12t$

Step 4: Answer the question.

The explicit expression that illustrates the amount of pressure of the gas in the container related to the time in minutes is,

Compare your answer with the correct one above

Question

There is an adjustable, cylindrical container in the science lab that is attached to a timer. The container holds a certain gas and the pressure of the gas in the container can be modeled by the function,

$P(s)=\frac{1}{4}+10s$

where is the size of the container.

Every minute the timer adjusts the size of the container and is modeled by the function,

where is in minutes.

Find an explicit expression that illustrates the amount of pressure of the gas in the container related to the time in minutes.

Answer

This question is testing one's ability to compose functions that are modeled by real world situations. Questions like these require in-depth critical reasoning skills and the ability to identify the meaning of composition of functions as they relate to scenarios.

For the purpose of Common Core Standards, composed functions falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A). Questions in this cluster depend heavily of building an understanding between real life situations as seen through a mathematical perspective.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what the question is asking for.

Step 2: Identify what is given/known from the question.

Step 3: Using algebraic methods creating function to describe relationship.

Step 4: Answer the question.

Following the steps listed above for this particular problem is as follows.

Step 1: Identify what the question is asking for.

The question is asking to find the composition of the two functions.

In other words, find .

Step 2: Identify what is given/known from the question.

The two functions are given in mathematical form.

$P(s)=\frac{1}{4}+10s$

Step 3: Using algebraic methods creating function to describe relationship.

To solve this problem, replace every in the pressure function with the entire function .

$\P(S(t))=\frac{1}{4}+10(10-2t) \ \P(S(t))=\frac{1}{4}+100-20t \ \P(S(t))=100.25-20t$

Step 4: Answer the question.

The explicit expression that illustrates the amount of pressure of the gas in the container related to the time in minutes is,

Compare your answer with the correct one above

Question

There is an adjustable, cylindrical container in the science lab that is attached to a timer. The container holds a certain gas and the pressure of the gas in the container can be modeled by the function,

$P(s)=\frac{1}{6}+8s$

where is the size of the container.

Every minute the timer adjusts the size of the container and is modeled by the function,

where is in minutes.

Find an explicit expression that illustrates the amount of pressure of the gas in the container related to the time in minutes.

Answer

This question is testing one's ability to compose functions that are modeled by real world situations. Questions like these require in-depth critical reasoning skills and the ability to identify the meaning of composition of functions as they relate to scenarios.

For the purpose of Common Core Standards, composed functions falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A). Questions in this cluster depend heavily of building an understanding between real life situations as seen through a mathematical perspective.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what the question is asking for.

Step 2: Identify what is given/known from the question.

Step 3: Using algebraic methods creating function to describe relationship.

Step 4: Answer the question.

Following the steps listed above for this particular problem is as follows.

Step 1: Identify what the question is asking for.

The question is asking to find the composition of the two functions.

In other words, find .

Step 2: Identify what is given/known from the question.

The two functions are given in mathematical form.

$P(s)=\frac{1}{6}+8s$

Step 3: Using algebraic methods creating function to describe relationship.

To solve this problem, replace every in the pressure function with the entire function .

$\P(S(t))=\frac{1}{6}+8(10-2t) \ \P(S(t))=\frac{1}{6}+80-16t \ \P(S(t))=80.1\overline{6}-16t$

Step 4: Answer the question.

The explicit expression that illustrates the amount of pressure of the gas in the container related to the time in minutes is,

$P(S(t))=80.\overline{6}-16t$

Compare your answer with the correct one above

Question

There is an adjustable, cylindrical container in the science lab that is attached to a timer. The container holds a certain gas and the pressure of the gas in the container can be modeled by the function,

$P(s)=\frac{1}{6}+8s$

where is the size of the container.

Every minute the timer adjusts the size of the container and is modeled by the function,

where is in minutes.

Find an explicit expression that illustrates the amount of pressure of the gas in the container related to the time in minutes.

Answer

This question is testing one's ability to compose functions that are modeled by real world situations. Questions like these require in-depth critical reasoning skills and the ability to identify the meaning of composition of functions as they relate to scenarios.

For the purpose of Common Core Standards, composed functions falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A). Questions in this cluster depend heavily of building an understanding between real life situations as seen through a mathematical perspective.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what the question is asking for.

Step 2: Identify what is given/known from the question.

Step 3: Using algebraic methods creating function to describe relationship.

Step 4: Answer the question.

Following the steps listed above for this particular problem is as follows.

Step 1: Identify what the question is asking for.

The question is asking to find the composition of the two functions.

In other words, find .

Step 2: Identify what is given/known from the question.

The two functions are given in mathematical form.

$P(s)=\frac{1}{6}+8s$

Step 3: Using algebraic methods creating function to describe relationship.

To solve this problem, replace every in the pressure function with the entire function .

$\P(S(t))=\frac{1}{6}+8(4-2t) \ \P(S(t))=\frac{1}{6}+32-16t \ \P(S(t))=32.\overline{6}-16t$

Step 4: Answer the question.

The explicit expression that illustrates the amount of pressure of the gas in the container related to the time in minutes is,

$P(S(t))=32.\overline{6}-16t$

Compare your answer with the correct one above

Question

There is an adjustable, cylindrical container in the science lab that is attached to a timer. The container holds a certain gas and the pressure of the gas in the container can be modeled by the function,

$P(s)=\frac{1}{2}+s$

where is the size of the container.

Every minute the timer adjusts the size of the container and is modeled by the function,

where is in minutes.

Find an explicit expression that illustrates the amount of pressure of the gas in the container related to the time in minutes.

Answer

This question is testing one's ability to compose functions that are modeled by real world situations. Questions like these require in-depth critical reasoning skills and the ability to identify the meaning of composition of functions as they relate to scenarios.

For the purpose of Common Core Standards, composed functions falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A). Questions in this cluster depend heavily of building an understanding between real life situations as seen through a mathematical perspective.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what the question is asking for.

Step 2: Identify what is given/known from the question.

Step 3: Using algebraic methods creating function to describe relationship.

Step 4: Answer the question.

Following the steps listed above for this particular problem is as follows.

Step 1: Identify what the question is asking for.

The question is asking to find the composition of the two functions.

In other words, find .

Step 2: Identify what is given/known from the question.

The two functions are given in mathematical form.

$P(s)=\frac{1}{2}+s$

Step 3: Using algebraic methods creating function to describe relationship.

To solve this problem, replace every in the pressure function with the entire function .

$\P(S(t))=\frac{1}{2}+(10-2t) \ \P(S(t))=\frac{1}{2}+10-2t \ \P(S(t))=10.5-2t$

Step 4: Answer the question.

The explicit expression that illustrates the amount of pressure of the gas in the container related to the time in minutes is,

Compare your answer with the correct one above

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