Cumulative Review Exercises (Chapters P–2)

1.
1. $\frac{y^{2}}{x^{3}}$ $\frac{y^{2}}{x^{3}}$
2. $\frac{1}{x + y}$ $\frac{1}{x + y}$
3.
1. $3 \sqrt{3}$ $3 \sqrt{3}$
2. $\frac{2 x}{(x + 1) (x + 2)}$ $\frac{2 x}{(x + 1) (x + 2)}$
5.
1. $x = 4$ $x = 4$
2. No solution
7.
1. $\frac{1}{4} \pm \frac{\sqrt{23}}{4} i$ $\frac{1}{4} \pm \frac{\sqrt{23}}{4} i$
2. $x = \frac{3}{2}$ $x = \frac{3}{2}$
9.
1. $x = \frac{7 + \sqrt{17}}{8}$ $x = \frac{7 + \sqrt{17}}{8}$
2. $x = 0; \frac{8}{9}$ $x = 0; \frac{8}{9}$
11.
1. (0, 4)
2. $[- 3, - 2]$ $[- 3, - 2]$
13. Because the length ofthe side BC is equal to the length of the side AC (which is 5), the triangle is isosceles.
15. All of the points satisfy the equation ${(x - 2)}^{2} + {(y + 1)}^{2} = 5^{2},$ ${(x - 2)}^{2} + {(y + 1)}^{2} = 5^{2},$ which is a circle with center $(2, - 1)$ $(2, - 1)$ and radius 5.
17. $y = - 3 x + 5$ $y = - 3 x + 5$
19. $y = - 0.5 x$ $y = - 0.5 x$
21. $y = - \frac{1}{4} x + 4$ $y = - \frac{1}{4} x + 4$
23. $x = 2$ $x = 2$
25.
27.
29. She purchased 60 books.
31.
1. $[- 1, \infty)$ $[- 1, \infty)$
2. x-intercept: 8; y-intercept: $- 2$ $- 2$
3. $- 3$ $- 3$
4. $(8, \infty)$ $(8, \infty)$
33.
1. $(f \circ g) (x) = \frac{x}{2 - 2 x},$ $(f \circ g) (x) = \frac{x}{2 - 2 x},$ and its domain is $(- \infty, 0) \cup (0, 1) \cup (1, \infty) .$ $(- \infty, 0) \cup (0, 1) \cup (1, \infty) .$
2. $(g \circ f) (x) = 2 (x - 2),$ $(g \circ f) (x) = 2 (x - 2),$ and its domain is $(- \infty, 2) \cup (2, \infty) .$ $(- \infty, 2) \cup (2, \infty) .$

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Table of Contents for Cumulative Review Exercises (Chapters P–2)