given the function below, fill in the table of values, use the table of values to graph the function, and…
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.\n\n$y = (x - 3)^3$\n\n| $x$ | $x - 3$ | $y = (x - 3)^3$ |\n| --- | --- | --- |\n| 1 | | |\n| 2 | | |\n| 3 | | |\n| 4 | | |\n| 5 | | |
Answer
Explanation:
Step1: Calculate $x-3$ for each $x$
For $x=1$: $1-3=-2$ For $x=2$: $2-3=-1$ For $x=3$: $3-3=0$ For $x=4$: $4-3=1$ For $x=5$: $5-3=2$
Step2: Calculate $y=(x-3)^3$
For $x=1$: $(-2)^3=-8$ For $x=2$: $(-1)^3=-1$ For $x=3$: $0^3=0$ For $x=4$: $1^3=1$ For $x=5$: $2^3=8$
Step3: Identify domain of $y=(x-3)^3$
Cubic polynomials accept all real numbers as inputs, so domain is all real $x$.
Step4: Identify range of $y=(x-3)^3$
Cubic polynomials output all real numbers, so range is all real $y$.
Answer:
Completed Table:
| $x$ | $x-3$ | $y=(x-3)^3$ |
|---|---|---|
| 1 | $-2$ | $-8$ |
| 2 | $-1$ | $-1$ |
| 3 | $0$ | $0$ |
| 4 | $1$ | $1$ |
| 5 | $2$ | $8$ |
Domain:
All real numbers, or $(-\infty, \infty)$
Range:
All real numbers, or $(-\infty, \infty)$