Lesson 5 Flipped Out Develop Understanding

Ready

Solve each equation for $y$ .

1.

$\frac{6}{7} x + \frac{3}{4} y = 15$

2.

$x^{2} - y^{2} + 4 x + 4 = 0$

3.

$\frac{x}{25} + \frac{y}{75} = 1$

4.

$x = \frac{y + 9}{6}$

5.

$2 x^{2} = x^{2} + 5 x y + 30$

6.

$3 y = 18 x - 3 x y$

Set

Create the inverse function for each of the functions provided. Represent the inverse in the same way the original function is given. If given as a graph, then provide a graph; if given as a table, then provide a table; if given ordered pairs, provide ordered pairs.

7.

Write the inverse function for the table of values.

Input: $x$	$- 10$	$- 6$	$- 2$	$2$	$6$
Output: $g (x)$	$- 2$	$- 1$	$0$	$1$	$2$

Input: $x$
Output: $g^{- 1} (x)$

8.

Write the inverse function for $f (x)$ .

$f (x) = {(- 13, 5), (- 9, - 9), (- 5, - 2), (- 1, - 5), (0, - 4), (4, 6), (9, 10), (14, 32)}$

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

9.

The function $g (x)$ is on the graph. Graph the inverse, $g^{- 1} (x)$ , on the same set of axes.

10.

Find the inverse function for the function given in the table.

$t$	$d (t)$
$- 2$	$5$
$- 1$	$7$
$0$	$9$
$1$	$11$
$2$	$13$

11.

I am going on a long trip to Barcelona, Spain. I am only taking one suitcase and it is packed very full. I plan to arrive completely exhausted at my hotel in the middle of the night. The only thing I will want to take out of my suitcase is a pair of pajamas. So, when I pack my suitcase at home, do I want to put my pajamas in first, somewhere in the middle, or last? Explain.

Go

Rewrite the expressions in equivalent form by using the distributive property to multiply, then combine like terms. Express the values under the square root symbol with the lowest possible value by removing perfect square factors.

12.

$\sqrt{3} (4 + 5 \sqrt{3})$

13.

$6 \sqrt{11} (2 - \sqrt{11})$

14.

$(1 - 7 \sqrt{2}) (1 - \sqrt{2})$

15.

$(3 + 2 \sqrt{13}) (3 - 2 \sqrt{13})$

16.

$(4 + 3 \sqrt{5}) (4 - 3 \sqrt{5})$

17.

$(1 - 3 \sqrt{6}) (5 - 2 \sqrt{6})$