Question

given the function below, fill in the table of values, use the table of values to graph the function, and then identify the function’s domain and range.

$y = -3x^3$

$x$	$x^3$	$y = -3x^3$
$-1$
$0$
$1$
$2$

Explanation:

Step1: Calculate $x^3$ for each $x$

For $x=-2$: $(-2)^3 = -8$
For $x=-1$: $(-1)^3 = -1$
For $x=0$: $0^3 = 0$
For $x=1$: $1^3 = 1$
For $x=2$: $2^3 = 8$

Step2: Calculate $y=-3x^3$ for each $x$

For $x=-2$: $y=-3\times(-8)=24$
For $x=-1$: $y=-3\times(-1)=3$
For $x=0$: $y=-3\times0=0$
For $x=1$: $y=-3\times1=-3$
For $x=2$: $y=-3\times8=-24$

Step3: Identify domain of $y=-3x^3$

Polynomial functions have no restrictions on input $x$, so all real numbers are allowed.

Step4: Identify range of $y=-3x^3$

Cubic polynomials output all real numbers as $x$ varies over all real numbers.

Answer:

Completed Table:

$x$	$x^3$	$y=-3x^3$
$-1$	$-1$	$3$
$0$	$0$	$0$
$1$	$1$	$-3$
$2$	$8$	$-24$

Domain:

All real numbers, or $(-\infty, \infty)$

Range:

All real numbers, or $(-\infty, \infty)$