1. Let's analyze the function A: $F(x) = x \sin x$. - Domain: $x$ can be any real number since $x$ and $\sin x$ are defined everywhere. - Range: Since $\sin x$ oscillates between $-1$ and $1$, $F(x)$ can take all values between $-\infty$ and $\infty$ as $x$ grows large positive or negative. 2. Analyze function B: $F(x) = \frac{1}{x} \sin x$. - Domain: $x \neq 0$ because $\frac{1}{x}$ is undefined at $0$. - Range: As $x$ approaches $0$, $F(x)$ oscillates and tends towards infinity in magnitude; for large $|x|$, $F(x)$ tends to $0$ since $\sin x$ is bounded. 3. Analyze function C: $F(x) = x + 5 \sin x$. - Domain: all real numbers since $x$ and $\sin x$ are defined everywhere. - Range: As $x$ increases or decreases, $x$ dominates, so range is $(-\infty, \infty)$. Summary: - A) Domain: $(-\infty, \infty)$, Range: $(-\infty, \infty)$ - B) Domain: $(-\infty, 0) \cup (0, \infty)$, Range is all real numbers due to oscillations and vertical asymptote at $x=0$. - C) Domain: $(-\infty, \infty)$, Range: $(-\infty, \infty)$