Lesson 3 Radical Thinking Develop Understanding

Ready

Fill in the table of values for each function.

1.

$f (x) = 3 x + 5$

$x$	$f (x)$
$- 1$
$0$
$1$
$2$
$3$

2.

$g (x) = 3 (x - 1) + 5$

$x$	$g (x)$
$- 1$
$0$
$1$
$2$
$3$

3.

$h (x) = 3 (x - 2) + 5$

$x$	$h (x)$
$- 1$
$0$
$1$
$2$
$3$

4.

$k (x) = 3 (x + 1) + 5$

$x$	$k (x)$
$- 1$
$0$
$1$
$2$
$3$

5.

$p (x) = (3) 2^{x}$

$x$	$p (x)$
$- 1$
$0$
$1$
$2$
$3$

6.

$q (x) = (3) 2^{(x - 1)}$

$x$	$q (x)$
$- 1$
$0$
$1$
$2$
$3$

7.

$r (x) = (3) 2^{(x - 2)}$

$x$	$r (x)$
$- 1$
$0$
$1$
$2$
$3$

8.

$s (x) = (3) 2^{(x + 1)}$

$x$	$s (x)$
$- 1$
$0$
$1$
$2$
$3$

9.

$h (x) = - 5 x + 2$

$x$	$h (x)$
$- 1$
$0$
$1$
$2$
$3$

10.

$h (x) = - 5 (x - 1) + 2$

$x$	$h (x)$
$- 1$
$0$
$1$
$2$
$3$

11.

$h (x) = - 5 (x - 2) + 2$

$x$	$h (x)$
$- 1$
$0$
$1$
$2$
$3$

12.

$h (x) = - 5 (x + 1) + 2$

$x$	$h (x)$
$- 1$
$0$
$1$
$2$
$3$

Set

Each of the expressions can be written using either radical notation, $\sqrt[n]{a^{m}}$ , or rational exponents, $a^{\frac{m}{n}}$ . Rewrite each of the given expressions in the form that is missing.

13.

Radical form: $\sqrt[3]{5^{2}}$

14.

Exponential form: $16^{\frac{3}{4}}$

15.

Radical form: $\sqrt[3]{5^{7} \cdot 3^{5}}$

16.

Exponential form: $9^{\frac{2}{3}} \cdot 9^{\frac{4}{3}}$

17.

Radical form: $\sqrt[5]{x^{13} y^{21}}$

18.

Radical form: $\sqrt[3]{27 a^{5} b^{2}}$

19.

Radical form: $\sqrt[5]{\frac{32 x^{13}}{243 y^{15}}}$

20.

Exponential form: $9^{\frac{3}{2}} s^{\frac{6}{3}} t^{\frac{1}{2}}$

Go

Given the function, find the $x$ -intercept(s) and $y$ -intercept if they exist, and then use them to graph the function.

21.

$f (x) = 5 (x - 4) - 10$

$x$ -intercept:

$y$ -intercept:

22.

$g (x) = 5 (2^{x - 1})$

$x$ -intercept:

$y$ -intercept:

23.

$h (x) = - 2 (x + 3)$

$x$ -intercept:

$y$ -intercept:

24.

$k (x) = 2 x - 8$

$x$ -intercept:

$y$ -intercept: