Lesson 2 Piece-Wiser Solidify Understanding

Ready

Solve each equation.

1.

$| x | = 7$

2.

$| x - 6 | = 3$

3.

$| w + 4 | = 11$

4.

$- 9 | m | = - 63$

5.

$| 3 d | = 15$

6.

$| 3 x - 5 | = 11$

7.

$- | m + 3 | = - 13$

8.

$| - 4 m | = 64$

9.

$2 | x + 1 | - 7 = - 3$

10.

$5 | c + 3 | - 1 = 9$

11.

$- 2 | 2 p - 3 | - 1 = - 11$

12.

Explain why the equation $| m | = - 3$ has no solution.

Set

State the domain and range of the piecewise functions in each graph below. Use interval notation.

13.

a.

Domain:

b.

Range:

14.

a.

Domain:

b.

Range:

Use the given piecewise function to answer the questions and sketch a graph.

15.

$g (x) = {\begin{matrix} {(x + 4)}^{2}, & - 6 \leq x \leq - 2 \\ - 2 x + 6, & 0 \leq x \leq 2 \\ \frac{1}{2} x - 1, & 2 < x \leq 6 \end{matrix}$

a.

Find $g (1)$ .

b.

Find $g (4)$ .

c.

Find $g (- 5)$ .

d.

Find $g (x) = 6$ .

e.

Sketch a graph of this function.

16.

$h (x) = {\begin{matrix} {(x + 4)}^{2}, & x \leq - 2 \\ - 2 x, & - 2 < x \leq 0 \\ 2 x, & 0 < x \leq 2 \\ {(x - 4)}^{2}, & x > 2 \end{matrix}$

a.

Find $h (- 1)$ .

b.

Find $h (7)$ .

c.

Find $h (3)$ .

d.

Find $h (x) = 0$ .

e.

Sketch a graph of this function.

Write the piecewise equations for the given graphs.

17.

18.

Go

Beginning with the parent function $f (x) = x^{2}$ , write the equation of the new function, $g (x)$ , that is a transformation of $f (x)$ as described. Then graph it.

19.

Shift $f (x)$ left $3$ units, stretch vertically by $2$ , reflect vertically, and shift down $5$ units.

$g (x) = \underset{―}{}$

20.

Shift $f (x)$ right $1$ , stretch vertically by $3$ , and shift up $4$ units.

$g (x) = \underset{―}{}$

21.

Shift $f (x)$ up $3$ units, left $6$ , reflect vertically, and stretch by $\frac{1}{2}$ .

$g (x) = \underset{―}{}$