### All Common Core: High School - Functions Resources

## Example Questions

### Example Question #1 : Compose Functions: Ccss.Math.Content.Hsf Bf.A.1c

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,

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.

**Possible Answers:**

**Correct 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.

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

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

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,

### Example Question #2 : Compose Functions: Ccss.Math.Content.Hsf Bf.A.1c

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,

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.

**Possible Answers:**

**Correct 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.

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

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

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,

### Example Question #3 : Compose Functions: Ccss.Math.Content.Hsf Bf.A.1c

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,

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.

**Possible Answers:**

**Correct 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.

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

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

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,

### Example Question #4 : Compose Functions: Ccss.Math.Content.Hsf Bf.A.1c

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.

**Possible Answers:**

**Correct answer:**

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.

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

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

Step 4: Answer the question.

### Example Question #5 : Compose Functions: Ccss.Math.Content.Hsf Bf.A.1c

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.

**Possible Answers:**

**Correct answer:**

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.

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

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

Step 4: Answer the question.

### Example Question #6 : Compose Functions: Ccss.Math.Content.Hsf Bf.A.1c

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.

**Possible Answers:**

**Correct answer:**

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.

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

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

Step 4: Answer the question.

### Example Question #7 : Compose Functions: Ccss.Math.Content.Hsf Bf.A.1c

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.

**Possible Answers:**

**Correct answer:**

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.

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

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

Step 4: Answer the question.

### Example Question #8 : Compose Functions: Ccss.Math.Content.Hsf Bf.A.1c

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.

**Possible Answers:**

**Correct answer:**

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.

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

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

Step 4: Answer the question.

### Example Question #9 : Compose Functions: Ccss.Math.Content.Hsf Bf.A.1c

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.

**Possible Answers:**

**Correct answer:**

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.

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

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

Step 4: Answer the question.

### Example Question #10 : Compose Functions: Ccss.Math.Content.Hsf Bf.A.1c

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.

**Possible Answers:**

**Correct answer:**

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.

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

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

Step 4: Answer the question.

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