Give the domain and range of the function.
-$f(x)=\frac{1}{6} x^{2}$
A) Domain: $\left(-\infty, \frac{1}{6}\right)$; range: $(-\infty, 0)$
B) Domain: $(-\infty, \infty)$; range: $(-\infty, 0)$
C) Domain: $(-\infty, \infty)$; range: $(0, \infty)$
D) Domain: $(-\infty, \infty)$; range: $(-\infty, \infty)$

Question

Quizplus · Accepted Answer

The function $f(x)=\frac{1}{6} x^{2}$ is a quadratic function, which means its graph is a parabola opening upwards. The domain of any quadratic function is all real numbers, $(-\infty, \infty)$, because you can plug any real number into the function. The range is $(0, \infty)$ because the lowest value of $f(x)$ is 0 (when $x=0$), and it increases without bound as $x$ moves away from 0 in either direction.

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