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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

Example Question #51 : Building Functions

Given the function f(x)=x^2 identify the graphically effect $\frac{1}{2}f(x)$ creates.

Possible Answers:

$\frac{1}{2}f(x)$ widens the original function f(x)=x^2

$\frac{1}{2}f(x)$ moves the original function f(x)=x^2 down half a unit

$\frac{1}{2}f(x)$ moves the original function f(x)=x^2 up half a unit

$\frac{1}{2}f(x)$ narrows the original function f(x)=x^2

Correct answer:

$\frac{1}{2}f(x)$ widens the original function f(x)=x^2

Explanation:

This question is testing one's ability to identify the graphically transformation that algebraic manipulation to the function f(x) 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 f(x) .

Screen shot 2016 01 14 at 6.39.40 am

The function f(x) in the graph above has a -intercept at zero.

Step 2: Use technology to graph the new function $\frac{1}{2}f(x)$

Q10

The function $\frac{1}{2}f(x)$ in the graph above has a -intercept at zero and the graph widens.

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.

Q10 2

Step 4: Answer the question.

$\frac{1}{2}f(x)$ widens the original function f(x)=x^2

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Example Question #52 : Building Functions

Given the function f(x)=x^2 identify the graphically effect $\frac{1}{4}f(x)$ creates.

Possible Answers:

$\frac{1}{4}f(x)$ moves the original function f(x)=x^2 down four units

$\frac{1}{4}f(x)$ narrows the original function f(x)=x^2

$\frac{1}{4}f(x)$ moves the original function f(x)=x^2 up four units

$\frac{1}{4}f(x)$ widens the original function f(x)=x^2

Correct answer:

$\frac{1}{4}f(x)$ widens the original function f(x)=x^2

Explanation:

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

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 f(x) .

Screen shot 2016 01 14 at 6.39.40 am

The function f(x) in the graph above has a -intercept at zero.

Step 2: Use technology to graph the new function $\frac{1}{4}f(x)$

Q12

The function $\frac{1}{4}f(x)$ in the graph above has a -intercept at zero and the graph widens.

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.

Q12 2

Step 4: Answer the question.

$\frac{1}{4}f(x)$ widens the original function f(x)=x^2

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All Common Core: High School - Functions Resources

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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

All Common Core: High School - Functions Resources

Example Questions

Example Question #51 : Building Functions

Example Question #52 : Building Functions

All Common Core: High School - Functions Resources

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