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.

$y = (x - 3)^3$

$x$	$x - 3$	$y = (x - 3)^3$
2
3
4
5

Explanation:

Step1: Calculate $x-3$ for $x=1$

$1-3=-2$

Step2: Calculate $y=(x-3)^3$ for $x=1$

$(-2)^3=-8$

Step3: Calculate $x-3$ for $x=2$

$2-3=-1$

Step4: Calculate $y=(x-3)^3$ for $x=2$

$(-1)^3=-1$

Step5: Calculate $x-3$ for $x=3$

$3-3=0$

Step6: Calculate $y=(x-3)^3$ for $x=3$

$0^3=0$

Step7: Calculate $x-3$ for $x=4$

$4-3=1$

Step8: Calculate $y=(x-3)^3$ for $x=4$

$1^3=1$

Step9: Calculate $x-3$ for $x=5$

$5-3=2$

Step10: Calculate $y=(x-3)^3$ for $x=5$

$2^3=8$

Step11: Identify domain of cubic function

Cubic functions have no restrictions on input $x$, so domain is all real numbers.

Step12: Identify range of cubic function

Cubic functions output all real numbers, so range is all real numbers.

Answer:

Completed Table:

$x$	$x-3$	$y=(x-3)^3$
2	$-1$	$-1$
3	$0$	$0$
4	$1$	$1$
5	$2$	$8$

Domain:

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

Range:

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