Give the domain and range of the function.
-$f(x)=-\frac{1}{2} x^{2}$
A) Domain: $(-\infty, \infty)$; range: $(-\infty, 0)$
B) Domain: $(-\infty, \infty)$; range: $(-\infty, \infty)$
C) Domain: $\left(-\frac{1}{2}, \infty\right)$; range: $(-\infty, 0)$
D) Domain: $(-\infty, \infty)$; range: $(0, \infty)$

Question

Quizplus · Accepted Answer

The domain of $f(x)=-\frac{1}{2} x^{2}$ is all real numbers, $(-\infty, \infty)$, because there are no restrictions on the values that $x$ can take. The range is $(-\infty, 0)$ because the function is a downward-opening parabola with a vertex at the origin (0,0), meaning it only takes on negative values and zero.

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