Question

consider the following.

graph of a curve on a coordinate plane

use the vertical line test to determine whether the curve is the graph of a function of x.

• yes, the curve is a function of x.
• no, the curve is not a function of x.

if the curve is a function, state the domain and range. (enter your answers using interval notation. if the curve is not a function enter...)

• domain: -4,4 (marked incorrect)
• range: -4,3 (marked incorrect)

Explanation:

Step1: Determine the domain

The domain is the set of all x - values for which the function is defined. Looking at the graph, the leftmost point has an x - value of - 3 (since there is a closed dot at x=-3) and the rightmost point has an x - value of 2 (since there is a closed dot at x = 2). So, the domain is the interval from - 3 to 2, inclusive. In interval notation, this is $[-3,2]$.

Step2: Determine the range

The range is the set of all y - values that the function takes. The lowest y - value on the graph is - 3 (from the closed dot at (2, - 3)) and the highest y - value is 3 (from the peak of the graph). So, the range is the interval from - 3 to 3, inclusive. In interval notation, this is $[-3,3]$.

Answer:

Domain: $[-3, 2]$
Range: $[-3, 3]$