Lesson 4 Absolutely Transformed Practice Understanding

Ready

Solve each of the equations for the indicated variable.

1.

Solve for $x$ .

$5 x - 15 y = 20$

2.

Solve for $y$ .

$12 x - 2 y = 40$

3.

Solve for $x$ .

$y = - 3 x + 12$

4.

Solve for $h$ .

$A = \frac{1}{2} b h$

5.

Solve for $a$ .

$a^{2} + b^{2} = c^{2}$

6.

Solve for $r$ .

$A = π r^{2}$

Set

Use the given information to write the indicated form of the function.

7.

Piecewise equation.

$x$	$f (x)$
$- 1$	$9$
$0$	$6$
$1$	$3$
$2$	$0$
$3$	$3$
$4$	$6$

8.

Absolute value equation.

9.

Make a table of values. Be sure to include the vertex in the table.

$h (x) = 5 | x - 6 | - 8$

10.

Graph $f (x) = {\begin{cases} - \frac{2}{3} (x - 6) + 4, & x < 6 \\ \frac{2}{3} (x - 6) + 4, & x \geq 6 \end{cases}$

Graph each of the absolute value functions.

11.

$f (x) = | x - 3 | - 5$

12.

$g (x) = | x + 4 | - 2$

13.

$h (x) = - \frac{1}{2} | x + 5 | + 1$

14.

$r (x) = 3 | x - 4 | - 6$

Use the given graph of an absolute value function to write the equation for the function.

15.

16.

Go

Rewrite each expression by performing the indicated operation. Each new expression should contain only one square root.

17.

$(- 7 - 2 \sqrt{5}) + (6 + 8 \sqrt{5})$

18.

$(- 10 - \sqrt{13}) - (- 11 + 5 \sqrt{13})$

19.

$(4 - \sqrt{50}) + (7 + 3 \sqrt{18}) - (12 - 2 \sqrt{72})$

20.

$\sqrt{98} + \sqrt{8}$