Question

The values on both axes range from negative 10 to 10 in
increments of 1. The curve passes through the following: left
parenthesis negative 6 comma negative 8 right parenthesis, left
parenthesis 0 comma negative 5 right parenthesis, left
parenthesis 1 comma negative 4 right parenthesis, left
parenthesis 2 comma negative 1 right parenthesis, left
parenthesis 2 comma 0 right parenthesis, left parenthesis 2
comma 1 right parenthesis, left parenthesis 3 comma 4 right
parenthesis, left parenthesis 7 comma 7 right parenthesis, and
left parenthesis 10 comma 8.5 right parenthesis. All values are
approximate.
The domain and range of the function are both the set of all
real numbers.
The domain of the function is the set of all non-negative real
numbers and the range is the set of all real numbers.
The domain and range of the function are both the set of all
non-negative real numbers.
The domain of the function is the set of all real numbers and
the range is the set of all non-negative real numbers.

Answer 1

Choice 1 is correct: the domain and range are both all real numbers.

Reason: the graph includes x-values that are negative and positive (e.g. x = −6, 0, 1, 2, 3, 7, 10), so the domain is not restricted to non‑negative numbers; likewise the y‑values include negatives and positives (e.g. y = −8, −5, −4, −1, 0, 1, 4, 7, 8.5), so the range is not restricted to non‑negative numbers. Thus neither axis is limited to non‑negative values, so the only matching choice is that both domain and range are all real numbers.

Note: the listed points include several different y‑values for x = 2, so the plotted relation would fail the vertical‑line test and would not be a function as drawn. If the graph were intended to be a function, those multiple y‑values at x = 2 would be inconsistent.