Try It Yourself

Try It Yourself#

Exercise 1#

Simplify

Rewrite $\frac{3}{x - 1} - \frac{5}{2 x + 1}$ as a single ratio.

Exercise 2#

Expand

Expand $(8 x + 11) (2 x - 5)$ using the FOIL method.

Exercise 3#

Expand

Expand $5 x^{6} (3 x - 4)^{2}$ .

Exercise 4#

Expand

Expand $(1 + 3 x) (1 - 3 x) (2 + x)$ .

Exercise 5#

Factor

Factor $4 x^{5} - 25 x^{3}$ .

Exercise 6#

Simplify

\frac{2 x^{4} - 2 x^{3} - 12 x^{2}}{9 x^{2} - x^{4}}

by factoring both the numerator and the denominator. Assume that $x \neq 0$ and $x \neq 3$ .

Exercise 7#

Factor and Simplify

Factor and simplify $10 x (x + 2)^{5} - 5 x^{2} (x + 2)^{3}$ .

Exercise 8#

Sketch a line

Sketch the graph of the line defined by $y = \frac{1}{4} (x - 5) - 2$ . Use the fact that the line is described in point-slope form.

Exercise 9#

Solve an inequality

Find all values of $x$ such that $x^{2} - 16 > 0$ . Write your answer using interval notation.

Exercise 10#

Sketch a line

Sketch the graph of $f (x) = 12 x^{2} - x - 6$ by finding the $x$ and $y$ -intercepts (see Graphing, Example 6).

$Graph of $y=\sqrt{x}$$

Exercise 11#

Domain

Determine the domain of each of the following functions. Write your answer using interval notation.

$g (x) = \frac{x}{12 x^{2} - x - 6}$
$h (x) = \frac{x}{\sqrt{12 x^{2} - x - 6}}$

Try It Yourself

Contents

Try It Yourself#

Exercise 1#

Exercise 2#

Exercise 3#

Exercise 4#

Exercise 5#

Exercise 6#

Exercise 7#

Exercise 8#

Exercise 9#

Exercise 10#

Exercise 11#