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

## Example Questions

### Example Question #41 : Building Functions

Given the function identify the graphically effect creates.

**Possible Answers:**

moves the original function left two units

moves the original function down two units

moves the original function right two units

moves the original function up two units

**Correct answer:**

moves the original function down two units

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.

Step 4: Answer the question.

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

### Example Question #42 : Building Functions

Given the function identify the graphically effect creates.

**Possible Answers:**

moves the original function up three units

moves the original function down three units

moves the original function to the left three units

moves the original function to the right three units

**Correct answer:**

moves the original function up three units

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.

Step 4: Answer the question.

In other words, moves the original function up three 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 down four units

moves the original function to the left four units

moves the original function up four units

moves the original function to the right four units

**Correct answer:**

moves the original function up four units

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.

Step 4: Answer the question.

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.

**Possible Answers:**

moves the original function down five units

moves the original function left five units

moves the original function up five units

moves the original function right five units

**Correct answer:**

moves the original function down five units

*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).

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.

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 #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 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 right one unit

*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).

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.

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 #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 left one unit

moves the original function right one unit

moves the original function down one unit

moves the original function up one unit

**Correct answer:**

moves the original function left one unit

*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).

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.

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 #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 left two units

moves the original function down two units

moves the original function right two units

moves the original function up two units

**Correct answer:**

moves the original function left two units

*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).

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.

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 #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 three units

moves the original function right three units

moves the original function down three units

moves the original function up three units

**Correct answer:**

moves the original function right three units

*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).

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.

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 #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 up two units

narrows the original function

moves the original function down two units

widens the original function

**Correct answer:**

narrows the original function

*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).

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.

Step 4: Answer the question.

narrows the original function

### Example Question #8 : 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

moves the original function up three units

moves the original function down three units

widens the original function

**Correct answer:**

narrows the original function

*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).

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.

Step 4: Answer the question.

narrows the original function