Mastery Check Solutions

Show What You Know

Sort the parent functions by like domain and range.

absolute value
cube root
cubic

linear
quadratic

rational
square root

Group 1

$domain : \{x | x \in ℝ\} range : \{y | y \in ℝ\}$

Group 2

$domain : \{x | x \in ℝ\} range : \{y | y \in ℝ, y \geq 0\}$

Group 3

other

linear
cubic
cube root

absolute value
quadratic

square root
rational

Note

Remember to use your notes to look at the tables and graphs for a visual representation of the parent functions.

Name the quadrants and end behavior for the parent functions in Group 1.

The linear, cubic, and cube root parent functions are graphed in Quadrants 1 and 3. The end behavior for all of these functions is: As $x \to + \infty, f (x) \to + \infty$ , and as $x \to - \infty, f (x) \to - \infty$ .

Note

Q: For this group of functions, if the x-coordinate is positive, what is the y-coordinate?

A: Positive

Q: If the x-coordinate is negative, what is the y-coordinate?

A: Negative

Name the quadrants and end behavior for the parent functions in Group 2.

The absolute value and quadratic parent functions are graphed in Quadrants 1 and 2. The end behavior for both of these functions is: As $x \to + \infty, f (x) \to + \infty$ , and as $x \to - \infty, f (x) \to + \infty$ .

Note

Q: For Group 2, if the x-value is negative, what is the y-value? Explain.

A: The y-value is positive for these functions because when you square a number or find its absolute value, the result is a positive number.

Name the domain and range in set-builder notation as well as the end behavior for the parent functions in Group 3.

The square root parent function:
Domain: $\{x | x \in ℝ, x \geq 0\}$ , range: $\{y | y \in ℝ, y \geq 0\}$

End behavior:
As $x \to + \infty, f (x) \to + \infty$ , and as $x \to 0, f (x) \to 0$

The rational parent function:
domain: $\{x | x \in ℝ, x \neq 0\}$ , range: $\{y | y \in ℝ, y \neq 0\}$
Quadrant I: As $x \to + \infty, f (x) \to 0$ , and as $x \to 0, f (x) \to + \infty$
Quadrant III: As $x \to - \infty, f (x) \to 0$ , and as $x \to 0, f (x) \to - \infty$

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.

Name a parent function given the graph or equation: linear, absolute value, square root, cube root, quadratic, cubic, rational.
Name the domain and range of parent functions.
Graph/Sketch a parent function given the equation: linear, absolute value, square root, cube root, quadratic, cubic, rational.
Describe the end behavior of parent functions.