Question

a. the graph is a function since it passes the vertical line test
b. the graph is a not function since it passes the vertical line test
c. the graph is a function since it fails the vertical line test
d. the graph is a not function since it fails the vertical line test

1. what is the domain of the function?

a. 3,4 or 3≤x≤4
b. 2,3 or 2≤x≤3
c. 0,6 or 0≤x≤6
d. -6,6 or -6≤x≤6

Explanation:

Step1: Recall vertical - line test

A graph represents a function if and only if any vertical line intersects the graph at most once. If a vertical line intersects the graph more than once, the graph is not a function. So, a graph is a NOT function if it fails the vertical line test.

Step2: Recall domain definition

The domain of a function is the set of all possible x - values. Looking at the given graph, the left - most x - value is at \(x=-6\) and the right - most x - value is at \(x = 6\). So the domain is \([-6,6]\) or \(-6\leq x\leq6\).

Answer:

1. d. the graph is a NOT function since it fails the vertical line test
2. d. \([-6,6]\) or \(-6\leq x\leq6\)