Contents

Preface
1Prerequisites
2Equations and Inequalities
3Functions
4Linear Functions
5Polynomial and Rational Functions
6Exponential and Logarithmic Functions
7The Unit Circle: Sine and Cosine Functions
8Periodic Functions
9Trigonometric Identities and Equations
10Further Applications of Trigonometry
11Systems of Equations and Inequalities
12Analytic Geometry
13Sequences, Probability, and Counting Theory
AProofs, Identities, and Toolkit Functions
Answer Key
Index

Practice Test

Graph the following: $2 y = 3 x + 4. 2 y = 3 x + 4.$

Find the x- and y-intercepts for the following: $2x-5y=6$

Find the x- and y-intercepts of this equation, and sketch the graph of the line using just the intercepts plotted.

$3 x - 4 y = 12 3 x - 4 y = 12$

Find the exact distance between $(5, −3) (5, −3)$ and $(- 2, 8) . (- 2, 8) .$ Find the coordinates of the midpoint of the line segment joining the two points.

Write the interval notation for the set of numbers represented by ${x | x \leq 9} . {x | x \leq 9} .$

Solve for x: $5 x + 8 = 3 x - 10. 5 x + 8 = 3 x - 10.$

Solve for $x x$ : $3 (2 x - 5) - 3 (x - 7) = 2 x - 9. 3 (2 x - 5) - 3 (x - 7) = 2 x - 9.$

Solve for x: $\frac{x}{2} + 1 = \frac{4}{x} \frac{x}{2} + 1 = \frac{4}{x}$

Solve for x: $\frac{5}{x + 4} = 4 + \frac{3}{x - 2} . \frac{5}{x + 4} = 4 + \frac{3}{x - 2} .$

10.

The perimeter of a triangle is 30 in. The longest side is 2 less than 3 times the shortest side and the other side is 2 more than twice the shortest side. Find the length of each side.

11.

Solve for x. Write the answer in simplest radical form.

$\frac{x^{2}}{3} - x = - \frac{1}{2} \frac{x^{2}}{3} - x = - \frac{1}{2}$

12.

Solve: $3 x - 8 \leq 4. 3 x - 8 \leq 4.$

13.

Solve: $| 2 x + 3 | < 5. | 2 x + 3 | < 5.$

14.

Solve: $| 3 x - 2 | \geq 4. | 3 x - 2 | \geq 4.$

For the following exercises, find the equation of the line with the given information.

15.

Passes through the points $(- 4, 2) (- 4, 2)$ and $(5, −3) . (5, −3) .$

16.

Has an undefined slope and passes through the point $(4, 3) . (4, 3) .$

17.

Passes through the point $(2, 1) (2, 1)$ and is perpendicular to $y = - \frac{2}{5} x + 3. y = - \frac{2}{5} x + 3.$

18.

Add these complex numbers: $(3 - 2 i) + (4 - i) . (3 - 2 i) + (4 - i) .$

19.

Simplify: $\sqrt{−4} + 3 \sqrt{−16} . \sqrt{−4} + 3 \sqrt{−16} .$

20.

Multiply: $5 i (5 - 3 i) . 5 i (5 - 3 i) .$

21.

Divide: $\frac{4 - i}{2 + 3 i} . \frac{4 - i}{2 + 3 i} .$

22.

Solve this quadratic equation and write the two complex roots in $a + b i a + b i$ form: $x^{2} - 4 x + 7 = 0. x^{2} - 4 x + 7 = 0.$

23.

Solve: ${(3 x - 1)}^{2} - 1 = 24. {(3 x - 1)}^{2} - 1 = 24.$

24.

Solve: $x^{2} - 6 x = 13. x^{2} - 6 x = 13.$

25.

Solve: $4 x^{2} - 4 x - 1 = 0 4 x^{2} - 4 x - 1 = 0$

26.

Solve: $\sqrt{x - 7} = x - 7 \sqrt{x - 7} = x - 7$

27.

Solve: $2 + \sqrt{12 - 2 x} = x 2 + \sqrt{12 - 2 x} = x$

28.

Solve: ${(x - 1)}^{\frac{2}{3}} = 9 {(x - 1)}^{\frac{2}{3}} = 9$

For the following exercises, find the real solutions of each equation by factoring.

29.

$2 x^{3} - x^{2} - 8 x + 4 = 0 2 x^{3} - x^{2} - 8 x + 4 = 0$

30.

${(x + 5)}^{2} - 3 (x + 5) - 4 = 0 {(x + 5)}^{2} - 3 (x + 5) - 4 = 0$