BC Calculus
Multiple Choice Review Question for Chapter 1

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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
  3. 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. \( \pi \)
    4. Solution E
  4. 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. \( f(x) = (2x)^{\frac{1}{3}}\)
    5. Solution C
  5. 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. \( -2 \text{ and }4\)
    6. Solution B
  6. 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. \( g(x) = \log_3(1 - x)\)
    7. Solution A
  7. 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. \( 6\)
    8. Solution D
  8. 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. \( \{ y \mid 0 \leq y \leq 1 \} \)
    9. Solution A
  9. 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. \( 9 \)
    10. Solution E
  10. 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
    11. Solution B
  11. 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