Mastery Check Solutions

Show What You Know

Two students were given the equation $y = x^{2}$ and instructed to translate it so that h = 1, and k = 3. Then they needed to graph the inverse of the translated function. Both students have incorrect answers. Explain their errors and show the correct answer.

Student A

Student B

Student A error analysis: 
This student did not take the ± square root and half of the graph is missing

Student B error analysis: 
This student translated the graph after finding the inverse instead of before. For the inverse h = 3 and k = 1.

Note

You may need to graph the original function and the translated function to help determine Student A and Student B errors.

Equation for the translated function
$y = {(x - 1)}^{2} + 3$  

Inverse algebraically (optional): 
$\begin{array}{rcl} x & = & {(y - 1)}^{2} + 3 \\ x - 3 & = & {(y - 1)}^{2} \\ \sqrt{x - 3} & = & \sqrt{{(y - 1)}^{2}} \\ \pm \sqrt{x - 3} & = & y - 1 \\ y & = & \pm \sqrt{x - 3} + 1 \end{array}$

Graph of the inverse

Note

It is recommended that you use vertex form for quadratic equations to write the transformed function. You can either solve for the inverse algebraically and then graph, or start by graphing.

Say What You Know

In your own words, talk about what you have learned using the objectives for this part of the lesson and your work on this page.

Note

Restate the objectives of the lesson in your own words. If you are unable to restate the lesson objectives, go back and reread the objectives and then explain them.

Graph a function and its inverse on the same coordinate plane and determine if they are functions. 
Use the horizontal line test to determine if the graph of an inverse is a function.

To continue, return to the Online Lesson.