Mastery Check

Show What You Know

Sketch a function with the following properties:

A domain and range of all real numbers
As $x \to + \infty, f (x) \to - \infty,$ and as $x \to - \infty, f (x) \to + \infty$
Contains a radical symbol
The point $(h, k)$ is $(4, 2)$
Passes through $(3, 4)$ and $(5, 0)$

Write the equation for the function you sketched in Part A.

$y = - 2 \sqrt[3]{x - 4} + 2$

Write an equation for a transformed absolute value function with the following properties:

The point $(h, k)$ in Quadrant IV

Note

Q: What do you know about the ordered pair if the vertex is in the fourth quadrant?
A: The x-coordinate is positive and the y-coordinate is negative.

The range $[- 6, \infty)$

Note

Q: What do you know about the function from the range?
A: The y-coordinate of the vertex.

The x-intercepts are the origin and $(6, 0)$

Note

The axis of symmetry is $x = 3 .$ The vertex is $(3, - 6)$

Dilates by a factor of 2.

Note

Q: What will the value of a be for the absolute value function?
A: $a = 2$

$y = 2 |x - 3| - 6$

Note

You may wish to sketch the equation and/or use technology before finalizing your equation. You need to consider each property and may need to skip around rather than considering the properties in the order they have been given.

Q: What is the end behavior for your function?

A: As $x \to + \infty, f (x) \to + \infty,$ and as $x \to - \infty, f (x) \to + \infty$

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.

- Transform parent functions (vertical, horizontal, dilation) on the coordinate plane.
- Write the equation of the transformed function given the graph or description.
- Name the domain and range of transformed parent functions.
- Name the end behavior of transformed parent functions.
- Describe how a parent function is being transformed without graphing.