BC Calculus Multiple Choice Review Question for Chapter 1

• Class: 5H: BC Calculus\)
• Author: Peter Atlas\)
• Text: Calculus Finney, Demana, Waits, Kennedy\)

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1. The domain of $$g(x) = \frac{\sqrt{x - 2}}{x^2 - x}$$ is
1. $$x \neq {0, 1}$$
2. $$x \leq 2, x \neq {0, 1}$$
3. $$x \leq 2$$
4. $$x \geq 2$$
5. $$x > 2$$
Solution D
2. Which of the following equations has a graph that is symmetric with respect to the origin?
1. $$y = \frac{x - 1}{x}$$
2. $$y = 2x^4 + 1$$
3. $$y = x^3 + 2x$$
4. $$y = x^3 + 2$$
5. $$y = \frac{x}{x^3 + 1}$$
3. Solution C
4. Let $$g(x) = |\cos{x} - 1|$$. The maximum value attained by $$g$$ on the closed interval $$[0, 2\pi]$$ is for $$x =$$
1. $$-1$$
2. $$0$$
3. $$\frac{\pi}{2}$$
4. $$2$$
5. $$\pi$$
5. Solution E
6. Which of the following functions is not odd?
1. $$f(x) = \sin{x}$$
2. $$f(x) = \sin {(2x)}$$
3. $$f(x) = x^3 + 1$$
4. $$f(x) = \frac{x}{x^2 + 1}$$
5. $$f(x) = (2x)^{\frac{1}{3}}$$
7. Solution C
8. The roots of the equation $$f(x) = 0$$ are 1 and -2. The roots of $$f(2x) = 0$$ are
1. $$1 \text{ and }-2$$
2. $$\frac{1}{2} \text{ and }-1$$
3. $$-\frac{1}{2} \text{ and }1$$
4. $$2 \text{ and }-4$$
5. $$-2 \text{ and }4$$
9. Solution B
10. The function whose graph is a reflection in the y-axis of the graph of $$f(x) = 1 - 3^x$$ is
1. $$g(x) = 1 - 3^{-x}$$
2. $$g(x) = 1 + 3^x$$
3. $$g(x) = 3^x - 1$$
4. $$g(x) = \log_3(x - 1)$$
5. $$g(x) = \log_3(1 - x)$$
11. Solution A
12. The period of $$\sin{(\frac{2\pi x}{3})}$$ is
1. $$\frac{1}{3}$$
2. $$\frac{2}{3}$$
3. $$\frac{3}{2}$$
4. $$3$$
5. $$6$$
13. Solution D
14. The range of $$y = f(x) = \ln{(\cos{x})}$$ is
1. $$\{ y \mid -\infty < y \leq 0 \}$$
2. $$\{ y \mid 0 < y \leq 1 \}$$
3. $$\{ y \mid -1 < y < 1 \}$$
4. $$\{ y \mid -\frac{\pi}{2} < y < \frac{\pi}{2} \}$$
5. $$\{ y \mid 0 \leq y \leq 1 \}$$
15. Solution A
16. If $$log_b (3^b) = \frac{b}{2}$$, then $$b =$$
1. $$\frac{1}{9}$$
2. $$\frac{1}{3}$$
3. $$\frac{1}{2}$$
4. $$3$$
5. $$9$$
17. Solution E
18. If the domain of $$f$$ is restricted to the open interval $$(-\frac{\pi}{2}, \frac{\pi}{2})$$, then the range of $$f(x) = e^{\tan{x}}$$ is
1. the set of all reals
2. the set of positive reals
3. the set of nonnegative reals
4. $$\{y \mid 0 < f(x) \leq 1\}$$
5. none of the preceeding
19. Solution B
20. Which of the following is a reflection of the graph of $$y = f(x)$$ in the x-axis?
1. $$y = -f(x)$$
2. $$y = f(-x)$$
3. $$y = \mid f(x)\mid$$
4. $$y = f(\mid x\mid)$$
5. $$y = -f(-x)$$
Solution A