Question

which one is the graph of $f(x)=x^3$? what is its range?
which one is the graph of $?(x)=x^3$? choose the correct graph below.
a.
b.
c.
d.
e.
f.
g.
h.
what is its range?
(type your answer in interval notation.)

Explanation:

Step1: Identify cubic function shape

The function $f(x)=x^3$ is a cubic polynomial. It has a characteristic S-shaped curve, increasing for all real $x$, passing through the origin $(0,0)$. Among the options, Graph A matches this shape: it is increasing, has the cubic curve form, and spans positive/negative $x,y$ values.

Step2: Determine the range

For $f(x)=x^3$, as $x\to+\infty$, $f(x)\to+\infty$; as $x\to-\infty$, $f(x)\to-\infty$. All real numbers are achievable as outputs.

Answer:

Correct graph: A. <The graph labeled A with the S-shaped cubic curve>
Range: $(-\infty, \infty)$