Lesson 5 Translating My Composition Solidify Understanding

Ready

Use the table to find the indicated function values.

$x$	$f (x)$	$g (x)$
$- 2$	$2$	$3$
$- 1$	$1$	$- 2$
$0$	$3$	$- 24$
$1$	$- 1$	$- 1$
$2$	$0$	$- 8$
$3$	$19$	$0$

1.

$f (g (3)) =$

2.

$f (g (1)) =$

3.

$g (f (- 2)) =$

4.

$g (f (- 1)) =$

5.

$g (f (0)) =$

6.

$g (g (- 2)) =$

7.

$f (f (0)) =$

8.

$g (f (1)) =$

9.

Do the graphs of $f (x)$ and $g (x)$ described in the table ever intersect each other? How do you know?

Use the graph to find the indicated values.

10.

$f (g (- 2)) =$

11.

$f (g (- 1)) =$

12.

$f (g (0.5)) =$

13.

$f (f (0)) =$

Set

Let $f (x) = x^{2}$ , $g (x) = 5 x$ , and $h (x) = \sqrt{x} + 2$ .

Express each function as a composite of $f$ , $g$ , and/or $h$ .

14.

$F (x) = x^{4}$

15.

$G (x) = 5 x^{2}$

16.

$P (x) = x + 2$

17.

$R (x) = 5 \sqrt{x} + 10$

18.

$Q (x) = 25 x$

19.

$H (x) = 25 x^{2}$

20.

$D (x) = \sqrt{\sqrt{(x)} + 2} + 2$

21.

$B (x) = x + 4 \sqrt{x} + 4$

22.

$K (x) = \sqrt{5 x} + 2$

Go

23.

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$y = \log_{2} x$
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$y = 3 + \log_{2} x$
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$y = 1 - \log_{2} x$
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$y = \log_{2} (x - 3)$