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

## Example Questions

### Example Question #1 : Identifying Function By Reading Inverse Graph: Ccss.Math.Content.Hsf Bf.B.4c

Which graph represents the the inverse of the following function?

**Possible Answers:**

**Correct answer:**

This question is testing ones ability to recognize and construct a function's inverse from its graph.

For the purpose of Common Core Standards, "Read values of an inverse function from a graph or a table, given that the function has an inverse." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4c). It is important to note that this standard is not directly tested on but is used for building a deeper understanding on inverses and their functions.

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: Identify what it means to be an inverse.

An inverse function is found algebraically as follows.

Now solve for the variable in the new (inverse) function.

Graphically, the inverse is the mirror image reflected over the line of symmetry. In other words, the coordinate pair components are switched.

Step 2: Construct coordinate pairs of the given graph.

Looking at the graph above, the following table of coordinate pairs can be constructed.

Step 3: Swap the points with the points to create the coordinate pairs of the inverse graph.

Step 4: Graph the inverse function.

### Example Question #2 : Identifying Function By Reading Inverse Graph: Ccss.Math.Content.Hsf Bf.B.4c

Which graph represents the the inverse of the following function?

**Possible Answers:**

**Correct answer:**

This question is testing ones ability to recognize and construct a function's inverse from its graph.

For the purpose of Common Core Standards, "Read values of an inverse function from a graph or a table, given that the function has an inverse." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4c). It is important to note that this standard is not directly tested on but is used for building a deeper understanding on inverses and their functions.

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: Identify what it means to be an inverse.

An inverse function is found algebraically as follows.

Now solve for the variable in the new (inverse) function.

Graphically, the inverse is the mirror image reflected over the line of symmetry. In other words, the coordinate pair components are switched.

Step 2: Construct coordinate pairs of the given graph.

Looking at the graph above, the following table of coordinate pairs can be constructed.

Step 3: Swap the points with the points to create the coordinate pairs of the inverse graph.

Step 4: Graph the inverse function.

### Example Question #3 : Identifying Function By Reading Inverse Graph: Ccss.Math.Content.Hsf Bf.B.4c

Which graph represents the the inverse of the following function?

**Possible Answers:**

**Correct answer:**

This question is testing ones ability to recognize and construct a function's inverse from its graph.

For the purpose of Common Core Standards, "Read values of an inverse function from a graph or a table, given that the function has an inverse." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4c). It is important to note that this standard is not directly tested on but is used for building a deeper understanding on inverses and their functions.

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: Identify what it means to be an inverse.

An inverse function is found algebraically as follows.

Now solve for the variable in the new (inverse) function.

Graphically, the inverse is the mirror image reflected over the line of symmetry. In other words, the coordinate pair components are switched.

Step 2: Construct coordinate pairs of the given graph.

Looking at the graph above, the following table of coordinate pairs can be constructed.

Step 3: Swap the points with the points to create the coordinate pairs of the inverse graph.

Step 4: Graph the inverse function.

### Example Question #4 : Identifying Function By Reading Inverse Graph: Ccss.Math.Content.Hsf Bf.B.4c

Which graph represents the the inverse of the following function?

**Possible Answers:**

**Correct answer:**

Step 1: Identify what it means to be an inverse.

An inverse function is found algebraically as follows.

Now solve for the variable in the new (inverse) function.

Step 2: Construct coordinate pairs of the given graph.

Looking at the graph above, the following table of coordinate pairs can be constructed.

Step 3: Swap the points with the points to create the coordinate pairs of the inverse graph.

Step 4: Graph the inverse function.

### Example Question #5 : Identifying Function By Reading Inverse Graph: Ccss.Math.Content.Hsf Bf.B.4c

Which graph represents the the inverse of the following function?

**Possible Answers:**

**Correct answer:**

Step 1: Identify what it means to be an inverse.

An inverse function is found algebraically as follows.

Now solve for the variable in the new (inverse) function.

Step 2: Construct coordinate pairs of the given graph.

Looking at the graph above, the following table of coordinate pairs can be constructed.

Step 3: Swap the points with the points to create the coordinate pairs of the inverse graph.

Step 4: Graph the inverse function.

### Example Question #6 : Identifying Function By Reading Inverse Graph: Ccss.Math.Content.Hsf Bf.B.4c

Which graph represents the the inverse of the following function?

**Possible Answers:**

**Correct answer:**

Step 1: Identify what it means to be an inverse.

An inverse function is found algebraically as follows.

Now solve for the variable in the new (inverse) function.

Step 2: Construct coordinate pairs of the given graph.

Looking at the graph above, the following table of coordinate pairs can be constructed.

Step 3: Swap the points with the points to create the coordinate pairs of the inverse graph.

Step 4: Graph the inverse function.

### Example Question #7 : Identifying Function By Reading Inverse Graph: Ccss.Math.Content.Hsf Bf.B.4c

Which graph represents the the inverse of the following function?

**Possible Answers:**

**Correct answer:**

Step 1: Identify what it means to be an inverse.

An inverse function is found algebraically as follows.

Now solve for the variable in the new (inverse) function.

Step 2: Construct coordinate pairs of the given graph.

Looking at the graph above, the following table of coordinate pairs can be constructed.

Step 3: Swap the points with the points to create the coordinate pairs of the inverse graph.

Step 4: Graph the inverse function.

### Example Question #8 : Identifying Function By Reading Inverse Graph: Ccss.Math.Content.Hsf Bf.B.4c

Which graph represents the the inverse of the following function?

**Possible Answers:**

**Correct answer:**

Step 1: Identify what it means to be an inverse.

An inverse function is found algebraically as follows.

Now solve for the variable in the new (inverse) function.

Step 2: Construct coordinate pairs of the given graph.

Looking at the graph above, the following table of coordinate pairs can be constructed.

Step 3: Swap the points with the points to create the coordinate pairs of the inverse graph.

Step 4: Graph the inverse function.

### Example Question #9 : Identifying Function By Reading Inverse Graph: Ccss.Math.Content.Hsf Bf.B.4c

Which graph represents the the inverse of the following function?

**Possible Answers:**

**Correct answer:**

Step 1: Identify what it means to be an inverse.

An inverse function is found algebraically as follows.

Now solve for the variable in the new (inverse) function.

Step 2: Construct coordinate pairs of the given graph.

Looking at the graph above, the following table of coordinate pairs can be constructed.

Step 3: Swap the points with the points to create the coordinate pairs of the inverse graph.

Step 4: Graph the inverse function.

### Example Question #10 : Identifying Function By Reading Inverse Graph: Ccss.Math.Content.Hsf Bf.B.4c

Which graph represents the the inverse of the following function?

**Possible Answers:**

**Correct answer:**

Step 1: Identify what it means to be an inverse.

An inverse function is found algebraically as follows.

Now solve for the variable in the new (inverse) function.

Step 2: Construct coordinate pairs of the given graph.

Looking at the graph above, the following table of coordinate pairs can be constructed.

Step 3: Swap the points with the points to create the coordinate pairs of the inverse graph.

Step 4: Graph the inverse function.

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