Question

Graph the relation shown in the table. Is the relation a function? Why or why not?

A; No; a vertical line passes through two graphed points.

B; Yes; no horizontal line passes through two graphed points.

C; No; a horizontal line passes through two graphed points.

D; Yes; no vertical line passes through two graphed points.

Answer 1

Answer: D; Yes; no vertical line passes through two graphed points.

Explanation:

A graph is only considered a function if it passes the vertical line test. The vertical line test is basically when you put a vertical line on any point in the graph, it can’t pass through more than one graphed point. It can only touch the line once. That graph is considered a function because no two points touch a vertical line in the same x-value.

Answer 2

Option D.

Explanation:

A relation is a function if there exist a unique output for each input value. In other words a relation is a function if there exist a unique value of y for each value of x.

Vertical line test : According to the vertical line test if the graph of a relation intersect any vertical line at most once, then the relation is a function.

From the given table it clear that the ordered pairs of relation are(-5,-5), (-3,-3), (1,1) and (2,2).

For each value of x, there is a unique value of y. It means no vertical line passes through two graphed points. So, the given relation is a function.

Therefore, the correct option is D.