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Common Core: High School - Functions : Building Functions

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

Given the function f(x)=x^2 identify the graphically effect f(x)+4 creates.

Possible Answers:

f(x)+4 moves the original function f(x)=x^2 down four units

f(x)+4 moves the original function f(x)=x^2 to the right four units

f(x)+4 moves the original function f(x)=x^2 up four units

f(x)+4 moves the original function f(x)=x^2 to the left four units

Correct answer:

f(x)+4 moves the original function f(x)=x^2 up four units

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 f(x)+4 .

The function f(x)+4 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 f(x)=x^2 , the graphically effect f(x)+4 creates is a vertical shift upwards of four units.

Step 4: Answer the question.

In other words, f(x)+4 moves the original function f(x)=x^2 up four units.

Report an Error

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

Given the function f(x)=x^2 identify the graphically effect f(x)-5 creates.

Possible Answers:

f(x)-5 moves the original function f(x)=x^2 up five units

f(x)-5 moves the original function f(x)=x^2 left five units

f(x)-5 moves the original function f(x)=x^2 down five units

f(x)-5 moves the original function f(x)=x^2 right five units

Correct answer:

f(x)-5 moves the original function f(x)=x^2 down five units

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 f(x)-5

The function f(x)-5 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 f(x)=x^2 , the graphically effect f(x)-5 creates is a vertical shift down of five units.

Step 4: Answer the question.

In other words, f(x)-5 moves the original function f(x)=x^2 down five units.

Report an Error

Example Question #221 : High School: Functions

Given the function f(x)=x^2 identify the graphically effect f(x-1) creates.

Possible Answers:

f(x-1) moves the original function f(x)=x^2 down one unit

f(x-1) moves the original function f(x)=x^2 up one unit

f(x-1) moves the original function f(x)=x^2 right one unit

f(x-1) moves the original function f(x)=x^2 left one unit

Correct answer:

f(x-1) moves the original function f(x)=x^2 right one unit

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 f(x-1)

The function f(x-1) 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 f(x)=x^2 , the graphically effect f(x-1) creates is a phase shift to the right one unit.

Step 4: Answer the question.

In other words, f(x-1) moves the original function f(x)=x^2 right one unit.

Report an Error

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

Given the function f(x)=x^2 identify the graphically effect f(x+1) creates.

Possible Answers:

f(x+1) moves the original function f(x)=x^2 up one unit

f(x+1) moves the original function f(x)=x^2 right one unit

f(x+1) moves the original function f(x)=x^2 left one unit

f(x+1) moves the original function f(x)=x^2 down one unit

Correct answer:

f(x+1) moves the original function f(x)=x^2 left one unit

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 f(x+1)

The function f(x+1) 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 f(x)=x^2 , the graphically effect f(x+1) creates is a phase shift to the left one unit.

Step 4: Answer the question.

In other words, f(x+1) moves the original function f(x)=x^2 left one unit.

Report an Error

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

Given the function f(x)=x^2 identify the graphically effect f(x+2) creates.

Possible Answers:

f(x+2) moves the original function f(x)=x^2 right two units

f(x+2) moves the original function f(x)=x^2 left two units

f(x+2) moves the original function f(x)=x^2 up two units

f(x+2) moves the original function f(x)=x^2 down two units

Correct answer:

f(x+2) moves the original function f(x)=x^2 left two units

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 f(x+2)

The function f(x+2) 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 f(x)=x^2 , the graphically effect f(x+2) creates is a phase shift to the left two units.

Step 4: Answer the question.

In other words, f(x+2) moves the original function f(x)=x^2 left two units.

Report an Error

Example Question #8 : Identifying Graphs & Effects Of Function Manipulation: Ccss.Math.Content.Hsf Bf.B.3

Given the function f(x)=x^2 identify the graphically effect f(x-3) creates.

Possible Answers:

f(x-3) moves the original function f(x)=x^2 down three units

f(x-3) moves the original function f(x)=x^2 up three units

f(x-3) moves the original function f(x)=x^2 left three units

f(x-3) moves the original function f(x)=x^2 right three units

Correct answer:

f(x-3) moves the original function f(x)=x^2 right three units

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 f(x-3)

The function f(x-3) 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 f(x)=x^2 , the graphically effect f(x-3) creates is a phase shift to the right three units.

Step 4: Answer the question.

In other words, f(x-3) moves the original function f(x)=x^2 right three units.

Report an Error

Example Question #9 : Identifying Graphs & Effects Of Function Manipulation: Ccss.Math.Content.Hsf Bf.B.3

Given the function f(x)=x^2 identify the graphically effect 2f(x) creates.

Possible Answers:

2f(x) narrows the original function f(x)=x^2

2f(x) moves the original function f(x)=x^2 down two units

2f(x) moves the original function f(x)=x^2 up two units

2f(x) widens the original function f(x)=x^2

Correct answer:

2f(x) narrows 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 2f(x)

The function 2f(x) 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.

2f(x) narrows the original function f(x)=x^2

Report an Error

Example Question #10 : Identifying Graphs & Effects Of Function Manipulation: Ccss.Math.Content.Hsf Bf.B.3

Given the function f(x)=x^2 identify the graphically effect 3f(x) creates.

Possible Answers:

3f(x) widens the original function f(x)=x^2

3f(x) narrows the original function f(x)=x^2

3f(x) moves the original function f(x)=x^2 up three units

3f(x) moves the original function f(x)=x^2 down three units

Correct answer:

3f(x) narrows 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 3f(x)

Q11

The function 3f(x) 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.

3f(x) narrows the original function f(x)=x^2

Report an Error

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.

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

Report an Error

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

Report an Error

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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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Common Core: High School - Functions : Building Functions

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

All Common Core: High School - Functions Resources

Example Questions

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

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

Example Question #221 : High School: Functions

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

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

Example Question #8 : Identifying Graphs & Effects Of Function Manipulation: Ccss.Math.Content.Hsf Bf.B.3

Example Question #9 : Identifying Graphs & Effects Of Function Manipulation: Ccss.Math.Content.Hsf Bf.B.3

Example Question #10 : Identifying Graphs & Effects Of Function Manipulation: Ccss.Math.Content.Hsf Bf.B.3

Example Question #51 : Building Functions

Example Question #52 : Building Functions

All Common Core: High School - Functions Resources

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