1. The function $y = a \sin bx$ is an odd function because sine is an odd function, and multiplying by constants $a$ and $b$ does not change this property. Answer: A. odd 2. To find $\sin^{-1}(\sin(3\pi/4))$, note that $3\pi/4$ is in the second quadrant, but the range of $\sin^{-1}$ is $[-\pi/2, \pi/2]$. So we find the equivalent angle in this range: $\sin(3\pi/4) = \sin(\pi - 3\pi/4) = \sin(\pi/4)$. The inverse sine of this is $\pi/4$. Answer: B. $\pi/4$ 3. Given the point $(\pi, 0)$ on $y = \sin x$, the corresponding point on $y = a \sin b(x - h) + k$ is found by solving for $x$ in the transformed function: $x = \frac{\pi}{b} + h$, and $y = k$. Answer: A. $(\frac{\pi}{b} + h, k)$ 4. The domain of $y = \sec^{-1} x$ is $x \leq -1$ or $x \geq 1$ because secant inverse is defined only for $|x| \geq 1$. Answer: A. $x < -1$ or $x > 1$ 5. Differentiate $\cos^2 x - \sin^2 x$: $$\frac{d}{dx}(\cos^2 x - \sin^2 x) = 2\cos x (-\sin x) - 2\sin x \cos x = -2\sin 2x$$ Answer: B. $-2 \sin 2x$ 6. $y = \log_{1/2} x$ is the reflection of $y = \log_2 x$ on the x-axis because changing the base from 2 to $1/2$ reflects the graph. Answer: A. $\log_2 x$ 7. The asymptote of $y = 3 \cdot 2^{x-1} - 1$ is the horizontal line $y = -1$. Answer: D. $y = -1$ 8. The asymptote of $y = \log_{1/2} |x|$ is the vertical line $x = 0$. Answer: A. $x = 0$ 9. Given $(2,9)$ on $y = 3^x$, find corresponding point on $y = 2 \cdot 3^{x-1} + 2$: At $x=3$, $y = 2 \cdot 3^{3-1} + 2 = 2 \cdot 3^2 + 2 = 2 \cdot 9 + 2 = 20$. Answer: A. $(3, 20)$ 10. For $y = e^x - \ln x$, derivative is $y' = e^x - \frac{1}{x}$. At $x=2$, $y'(2) = e^2 - \frac{1}{2}$. Answer: D. $e^2 - \frac{1}{2}$