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

## 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.

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

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 .

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

Step 2: Use technology to graph the new function

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.

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

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.

moves the original function  to the left three units

moves the original function  up three units

moves the original function  down three units

moves the original function  to the right three units

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 .

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

Step 2: Use technology to graph the new function .

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.

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

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.

moves the original function  to the right four units

moves the original function  up four units

moves the original function  down four units

moves the original function  to the left four units

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 .

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

Step 2: Use technology to graph the new function .

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.

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

In other words,  moves the original function  up four 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.

moves the original function  up five units

moves the original function  down five units

moves the original function  left five units

moves the original function  right five units

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 .

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

Step 2: Use technology to graph the new function

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.

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

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.

moves the original function  down one unit

moves the original function  right one unit

moves the original function  up one unit

moves the original function  left one unit

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 .

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

Step 2: Use technology to graph the new function

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.

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

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.

moves the original function  down one unit

moves the original function  right one unit

moves the original function  left one unit

moves the original function  up one unit

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 .

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

Step 2: Use technology to graph the new function

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.

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

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

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

Given the function  identify the graphically effect  creates.

moves the original function  up two units

moves the original function  left two units

moves the original function  right two units

moves the original function  down two units

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 .

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

Step 2: Use technology to graph the new function

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.

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

In other words,  moves the original function  left two 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.

moves the original function  down three units

moves the original function  up three units

moves the original function  right three units

moves the original function  left three units

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 .

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

Step 2: Use technology to graph the new function

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.

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

In other words,  moves the original function  right three 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.

widens the original function

narrows the original function

moves the original function  down two units

moves the original function  up two units

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 .

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

Step 2: Use technology to graph the new function

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.

narrows the original function

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

Given the function  identify the graphically effect  creates.

moves the original function  up three units

widens the original function

narrows the original function

moves the original function  down three units

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 .

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

Step 2: Use technology to graph the new function

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.

narrows the original function

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