Answer:
no
Step-by-step explanation:
This graph does not represent a function because it does not pass the vertical line test.
The vertical line test is a method to determine if a relation is a function using the graph of the relation.
To run the vertical line test, you imagine a vertical line moving from left to right over the graph. If at any single position of the vertical line, the vertical line intersects more than 1 point on the graph, then the graph does not show a function.
To run the vertical line test on this graph, imagine a vertical line on the left side of the graph going through x = -7.
The vertical line moves to the right. From x = -7 to just to the left of x = -4, the line does not intersect the graph at all.
At x = -4, the line intersects 1 point of the graph.
From just right of x = -4 to just left of x = 4, the line intersects 2 points of the graph.
At x = 4, the vertical line intersects 1 point on the graph.
To the right of x = 4, the line does not intersect the graph any more.
The important part for deciding whether or not this graph is a function is from x just to the right of -4 to x just to the left of 4. A vertical line in any position that passes through an x value between x = -4 and x = 4 intersects 2 points on the graph. That means the graph is not a function.
