Question

does the table below define y as a function of x? if so, give the domain and range of f. if not, state why not.

x	-1	0	1	2	3
y	7	9	3	-3	-7

Explanation:

Step1: Check function definition

A function requires each $x$-value to map to exactly one $y$-value. In the table, every $x$-value ($-1, 0, 1, 2, 3$) has a unique corresponding $y$-value with no repeated $x$-values.

Step2: Identify the domain

The domain is the set of all input $x$-values.
Domain: $\{-1, 0, 1, 2, 3\}$

Step3: Identify the range

The range is the set of all output $y$-values.
Range: $\{-7, -3, 3, 7, 9\}$

Answer:

Yes, the table defines $y$ as a function of $x$, since each $x$-value corresponds to exactly one $y$-value.
Domain: $\{-1, 0, 1, 2, 3\}$
Range: $\{-7, -3, 3, 7, 9\}$