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.

Step 4: Answer the question.

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

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.

Step 4: Answer the question.

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

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.

Step 4: Answer the question.

In other words,  moves the original function  left 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 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.

Step 4: Answer the question.

In other words,  moves the original function  right 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 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.

Step 4: Answer the question.

 narrows the original function 

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.

Step 4: Answer the question.

 narrows the original function 

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 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.

Step 4: Answer the question.

 widens the original function 

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 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.

Step 4: Answer the question.

 widens the original function 

This question is testing one's ability to algebraically calculate the inverse of a given function. This also builds one's understanding of the concept of a function and its inverse at a basic level, graphing functions, and the Cartesian plane and its coordinate system.

For the purpose of Common Core Standards, finding the inverse of a simple function, falls within the Cluster B of build new functions from existing functions concept (CCSS.Math.content.HSF.BF.B).

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: Switch the  and  variables.

The given function is,

recall that  therefore,

.

Now switch the variables.

Step 2: Solve for .

Solving for  requires the use of algebraic operations to move constants from side to side. Remember to use the opposite operation to move a constant from one side to the other.

Step 3: Answer the question.

Recall that after the variable are switch, and  is solved for it is really the inverse of  that is being solved for thus, .

This question is testing one's ability to algebraically calculate the inverse of a given function. This also builds one's understanding of the concept of a function and its inverse at a basic level, graphing functions, and the Cartesian plane and its coordinate system.

For the purpose of Common Core Standards, finding the inverse of a simple function, falls within the Cluster B of build new functions from existing functions concept (CCSS.Math.content.HSF.BF.B).

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: Switch the  and  variables.

The given function is,

recall that  therefore,

.

Now switch the variables.

Step 2: Solve for .

Solving for  requires the use of algebraic operations to move constants from side to side. Remember to use the opposite operation to move a constant from one side to the other.

Step 3: Answer the question.

Recall that after the variable are switch, and  is solved for it is really the inverse of  that is being solved for thus, .