Lesson 7 Piece Out Practice Understanding

Ready

Identify the rate of change (include units).

1.

A maintenance company charges its customers using the following rule based on hours worked.

$c (h) = 45 h + 80$

2.

Sasha just started a new job that pays a $$ 200$ sign-up bonus for taking the job and will pay $$ 18$ per hour.

3.

A leaky faucet is allowing $\frac{1}{3}$ of a gallon of water to leak into the drain each hour.

4.

A bank account has regular withdrawals each month. The balance of the account is modeled with the following rule.

$b (t) = 3,500 - 150 t$

5.

The graph shows the value of a house over time.

Set

Describe the transformations on the parent function $f (x) = | x |$ , indicated by each equation. Then graph the function.

6.

$g (x) = | x + 7 | - 5$

7.

$h (x) = - | x + 3 | + 4$

8.

$k (x) = - 5 | x - 6 | + 9$

9.

$r (x) = | x - 2 | - 8$

Create an absolute value equation for each function graphed below.

10.

11.

Find the inverse of each function.

12.

$f (x) = x^{2}, x \geq 0; f^{- 1} (x) =$

13.

$g (x) = 2 x + 4; g^{- 1} (x) =$

14.

$f (x) = {(x + 1)}^{2}, x \geq - 1; f^{- 1} (x) =$

15.

$h (x) = \frac{1}{3} x + 6; h^{- 1} (x) =$

16.

$f (x) = {(- 3, 5) (- 2, - 9) (- 1, - 2) (0, - 5) (1, - 4) (2, 6) (3, 10) (4, 8)};$

$f^{- 1} (x) =$

Write the piecewise function rule for the following absolute value functions.

17.

$h (x) = | x + 3 |$

18.

$g (x) = 5 | x - 7 |$

Find the inverse of each function and graph it on the grid. (Hint: Use a table if needed.)

19.

$f (x) = x^{3} + 2$

20.

$p (x) = {(x - 5)}^{3}$

Go

Write the piecewise function rule for each graph.

21.

22.

Create the graph for the given piecewise function.

23.

$f (x) = {\begin{cases} 4 x + 12, & - 3 \leq x < - 1 \\ - 3 x + 9, & 1 \leq x < 4 \end{cases}$

24.

$f (x) = {\begin{cases} - \frac{1}{2} x + 3, & - 6 \leq x < - 2 \\ x^{2}, & - 2 \leq x < 2 \\ - 3 x + 10, & 2 \leq x < 6 \end{cases}$