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.

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.

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.

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.

This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.

For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.

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: Determine whether the function given is invertible or non-invertible.

Using technology to graph the function  results in the following graph.

This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.

Step 2: Make the function invertible by restricting the domain.

To make the given function an invertible function, restrict the domain to  which results in the following graph.

Step 3: Graph the inverse of the invertible function.

Swapping the coordinate pairs of the given graph results in the inverse.

The inverse graphed alone is as follows.

This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.

For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.

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: Determine whether the function given is invertible or non-invertible.

Using technology to graph the function  results in the following graph.

This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.

Step 2: Make the function invertible by restricting the domain.

To make the given function an invertible function, restrict the domain to  which results in the following graph.

Step 3: Graph the inverse of the invertible function.

Swapping the coordinate pairs of the given graph results in the inverse.

Therefore, the inverse of this function algebraically

.

This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.

For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.

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: Determine whether the function given is invertible or non-invertible.

Using technology to graph the function  results in the following graph.

This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.

Step 2: Make the function invertible by restricting the domain.

To make the given function an invertible function, restrict the domain to  which results in the following graph.

Step 3: Graph the inverse of the invertible function.

Swapping the coordinate pairs of the given graph results in the inverse.

Therefore, the inverse of this function algebraically is

.

This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.

For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.

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: Determine whether the function given is invertible or non-invertible.

Using technology to graph the function  results in the following graph.

This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.

Step 2: Make the function invertible by restricting the domain.

To make the given function an invertible function, restrict the domain to  which results in the following graph.

Step 3: Graph the inverse of the invertible function.

Swapping the coordinate pairs of the given graph results in the inverse.

Therefore, the inverse of this function algebraically is

This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.

For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.

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: Determine whether the function given is invertible or non-invertible.

Using technology to graph the function  results in the following graph.

This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.

Step 2: Make the function invertible by restricting the domain.

To make the given function an invertible function, restrict the domain to  which results in the following graph.

Step 3: Graph the inverse of the invertible function.

Swapping the coordinate pairs of the given graph results in the inverse.

Therefore, the inverse of this function algebraically is

This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.

For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.

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: Determine whether the function given is invertible or non-invertible.

Using technology to graph the function  results in the following graph.

This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.

Step 2: Make the function invertible by restricting the domain.

To make the given function an invertible function, restrict the domain to  which results in the following graph.

Step 3: Graph the inverse of the invertible function.

Swapping the coordinate pairs of the given graph results in the inverse.

Therefore, the inverse of this function algebraically is