Common Core: High School - Functions : Identifying Graphs & Effects of Function Manipulation: CCSS.Math.Content.HSF-BF.B.3

Study concepts, example questions & explanations for Common Core: High School - Functions

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All Common Core: High School - Functions Resources

6 Diagnostic Tests 82 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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Example Question #1 : Identifying Graphs & Effects Of Function Manipulation: Ccss.Math.Content.Hsf Bf.B.3

Given the function  identify the graphically effect  creates.

Possible Answers:

 moves the original function  right two units

 moves the original function  up two units

 moves the original function  left two units

 moves the original function  down two units

Correct answer:

 moves the original function  down two units

Explanation:

This question is testing one's ability to identify the graphically transformation that algebraic manipulation to the function  creates. 

For the purpose of Common Core Standards, "Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k ." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.3). 

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: Use technology to graph the function .

Screen shot 2016 01 14 at 6.39.40 am

The function  in the graph above has a -intercept at zero.

Step 2: Use technology to graph the new function 

Q2

The function  in the graph above has a -intercept at negative two.

Step 3: Compare and interpret the two graphs to identify the graphically effect.

When the two functions are plotted on the same graph where the original function is in blue and the shifted function is in orange is below.

Q2 2

Given the original function , the graphically effect  creates is a vertical shift down of two units.

Step 4: Answer the question.

In other words,  moves the original function  down two units.

Example Question #2 : Identifying Graphs & Effects Of Function Manipulation: Ccss.Math.Content.Hsf Bf.B.3

Given the function  identify the graphically effect  creates.

Possible Answers:

 moves the original function  to the right three units

 moves the original function  up three units

 moves the original function  to the left three units

 moves the original function  down three units

Correct answer:

 moves the original function  up three units

Explanation:

This question is testing one's ability to identify the graphically transformation that algebraic manipulation to the function  creates. 

For the purpose of Common Core Standards, "Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k ." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.3). 

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: Use technology to graph the function .

Screen shot 2016 01 14 at 6.39.40 am

The function  in the graph above has a -intercept at zero.

Step 2: Use technology to graph the new function .

Screen shot 2016 01 14 at 6.40.16 am

The function  in the graph above has a -intercept at three.

Step 3: Compare and interpret the two graphs to identify the graphically effect.

When the two functions are plotted on the same graph where the original function is in blue and the shifted function is in orange is below.

Screen shot 2016 01 14 at 6.40.49 am

Given the original function , the graphically effect  creates is a vertical shift upwards of three units.

Step 4: Answer the question.

In other words,  moves the original function  up three units.

 

Example Question #3 : Identifying Graphs & Effects Of Function Manipulation: Ccss.Math.Content.Hsf Bf.B.3

Given the function  identify the graphically effect  creates.

Possible Answers:

 moves the original function  to the right four units

 moves the original function  to the left four units

 moves the original function  up four units

 moves the original function  down four units

Correct answer:

 moves the original function  up four units

Explanation:

This question is testing one's ability to identify the graphically transformation that algebraic manipulation to the function  creates. 

For the purpose of Common Core Standards, "Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k ." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.3). 

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: Use technology to graph the function .

Screen shot 2016 01 14 at 6.39.40 am

The function  in the graph above has a -intercept at zero.

Step 2: Use technology to graph the new function .

Q3

The function  in the graph above has a -intercept at four.

Step 3: Compare and interpret the two graphs to identify the graphically effect.

When the two functions are plotted on the same graph where the original function is in blue and the shifted function is in orange is below.

Q3 2

Given the original function , the graphically effect  creates is a vertical shift upwards of four units.

Step 4: Answer the question.

In other words,  moves the original function  up four units.

Example Question #4 : Identifying Graphs & Effects Of Function Manipulation: Ccss.Math.Content.Hsf Bf.B.3

Given the function  identify the graphically effect  creates.

Possible Answers:

 moves the original function  down five units

 moves the original function  up five units

 moves the original function  left five units

 moves the original function  right five units

Correct answer:

 moves the original function  down five units

Explanation:

This question is testing one's ability to identify the graphically transformation that algebraic manipulation to the function  creates. 

For the purpose of Common Core Standards, "Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k ." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.3). 

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: Use technology to graph the function .

Screen shot 2016 01 14 at 6.39.40 am

The function  in the graph above has a -intercept at zero.

Step 2: Use technology to graph the new function 

Q4

The function  in the graph above has a -intercept at negative five.

Step 3: Compare and interpret the two graphs to identify the graphically effect.

When the two functions are plotted on the same graph where the original function is in blue and the shifted function is in orange is below.

Q4 2

Given the original function , the graphically effect  creates is a vertical shift down of five units.

Step 4: Answer the question.

In other words,  moves the original function  down five units.

Example Question #5 : Identifying Graphs & Effects Of Function Manipulation: Ccss.Math.Content.Hsf Bf.B.3

Given the function  identify the graphically effect  creates.

Possible Answers:

 moves the original function  up one unit

 moves the original function  left one unit

 moves the original function  right one unit

 moves the original function  down one unit

Correct answer:

 moves the original function  right one unit

Explanation:

This question is testing one's ability to identify the graphically transformation that algebraic manipulation to the function  creates. 

For the purpose of Common Core Standards, "Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k ." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.3). 

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: Use technology to graph the function .

Screen shot 2016 01 14 at 6.39.40 am

The function  in the graph above has a -intercept at zero.

Step 2: Use technology to graph the new function 

Q5

The function  in the graph above has a -intercept at one and the vertex is moved to the right one unit.

Step 3: Compare and interpret the two graphs to identify the graphically effect.

When the two functions are plotted on the same graph where the original function is in blue and the shifted function is in orange is below.

Q5 2

Given the original function , the graphically effect  creates is a phase shift to the right one unit.

Step 4: Answer the question.

In other words,  moves the original function  right one unit.

Example Question #6 : Identifying Graphs & Effects Of Function Manipulation: Ccss.Math.Content.Hsf Bf.B.3

Given the function  identify the graphically effect  creates.

Possible Answers:

 moves the original function  left one unit

 moves the original function  down one unit

 moves the original function  up one unit

 moves the original function  right one unit

Correct answer:

 moves the original function  left one unit

Explanation:

This question is testing one's ability to identify the graphically transformation that algebraic manipulation to the function  creates. 

For the purpose of Common Core Standards, "Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k ." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.3). 

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: Use technology to graph the function .

Screen shot 2016 01 14 at 6.39.40 am

The function  in the graph above has a -intercept at zero.

Step 2: Use technology to graph the new function 

Q6

The function  in the graph above has a -intercept at one and the vertex is moved to the left one unit.

Step 3: Compare and interpret the two graphs to identify the graphically effect.

When the two functions are plotted on the same graph where the original function is in blue and the shifted function is in orange is below.

Q6 2

Given the original function , the graphically effect  creates is a phase shift to the left one unit.

Step 4: Answer the question.

In other words,  moves the original function  left one unit.

Example Question #7 : Identifying Graphs & Effects Of Function Manipulation: Ccss.Math.Content.Hsf Bf.B.3

Given the function  identify the graphically effect  creates.

Possible Answers:

 moves the original function  right two units

 moves the original function  down two units

 moves the original function  left two units

 moves the original function  up two units

Correct answer:

 moves the original function  left two units

Explanation:

This question is testing one's ability to identify the graphically transformation that algebraic manipulation to the function  creates. 

For the purpose of Common Core Standards, "Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k ." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.3). 

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: Use technology to graph the function .

Screen shot 2016 01 14 at 6.39.40 am

The function  in the graph above has a -intercept at zero.

Step 2: Use technology to graph the new function 

Q7

The function  in the graph above has a -intercept at four and the vertex is moved to the left two unit.

Step 3: Compare and interpret the two graphs to identify the graphically effect.

When the two functions are plotted on the same graph where the original function is in blue and the shifted function is in orange is below.

Q7 2

Given the original function , the graphically effect  creates is a phase shift to the left two units.

Step 4: Answer the question.

In other words,  moves the original function  left two units.

Example Question #1 : Identifying Graphs & Effects Of Function Manipulation: Ccss.Math.Content.Hsf Bf.B.3

Given the function  identify the graphically effect  creates.

Possible Answers:

 moves the original function  right three units

 moves the original function  left three units

 moves the original function  up three units

 moves the original function  down three units

Correct answer:

 moves the original function  right three units

Explanation:

This question is testing one's ability to identify the graphically transformation that algebraic manipulation to the function  creates. 

For the purpose of Common Core Standards, "Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k ." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.3). 

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: Use technology to graph the function .

Screen shot 2016 01 14 at 6.39.40 am

The function  in the graph above has a -intercept at zero.

Step 2: Use technology to graph the new function 

Q8

The function  in the graph above has a -intercept at nine and the vertex is moved to the right three units.

Step 3: Compare and interpret the two graphs to identify the graphically effect.

When the two functions are plotted on the same graph where the original function is in blue and the shifted function is in orange is below.

Q8 2

Given the original function , the graphically effect  creates is a phase shift to the right three units.

Step 4: Answer the question.

In other words,  moves the original function  right three units.

Example Question #2 : Identifying Graphs & Effects Of Function Manipulation: Ccss.Math.Content.Hsf Bf.B.3

Given the function  identify the graphically effect  creates.

Possible Answers:

 widens the original function 

 moves the original function  down two units

 moves the original function  up two units

 narrows the original function 

Correct answer:

 narrows the original function 

Explanation:

This question is testing one's ability to identify the graphically transformation that algebraic manipulation to the function  creates. 

For the purpose of Common Core Standards, "Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k ." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.3). 

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: Use technology to graph the function .

Screen shot 2016 01 14 at 6.39.40 am

The function  in the graph above has a -intercept at zero.

Step 2: Use technology to graph the new function 

Q9

The function  in the graph above has a -intercept at zero and the graph narrows.

Step 3: Compare and interpret the two graphs to identify the graphically effect.

When the two functions are plotted on the same graph where the original function is in blue and the shifted function is in orange is below.

Q9 2

Step 4: Answer the question.

 narrows the original function 

Example Question #3 : Identifying Graphs & Effects Of Function Manipulation: Ccss.Math.Content.Hsf Bf.B.3

Given the function  identify the graphically effect  creates.

Possible Answers:

 narrows the original function 

 widens the original function 

 moves the original function  up three units

 moves the original function  down three units

Correct answer:

 narrows the original function 

Explanation:

This question is testing one's ability to identify the graphically transformation that algebraic manipulation to the function  creates. 

For the purpose of Common Core Standards, "Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k ." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.3). 

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: Use technology to graph the function .

Screen shot 2016 01 14 at 6.39.40 am

The function  in the graph above has a -intercept at zero.

Step 2: Use technology to graph the new function 

Q11

The function  in the graph above has a -intercept at zero and the graph narrows.

Step 3: Compare and interpret the two graphs to identify the graphically effect.

When the two functions are plotted on the same graph where the original function is in blue and the shifted function is in orange is below.

Q11 2

Step 4: Answer the question.

 narrows the original function 

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All Common Core: High School - Functions Resources

6 Diagnostic Tests 82 Practice Tests Question of the Day Flashcards Learn by Concept
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