Question

36 which graph represents y as a function of x ?

Explanation:

Step1: Recall the vertical line test

A graph represents \( y \) as a function of \( x \) if no vertical line intersects the graph more than once. This is because for a function, each input \( x \) should have exactly one output \( y \).

Step2: Analyze Graph A

For Graph A, if we draw a vertical line (e.g., \( x = -1 \)), it will intersect the graph at two points (one on the upper curve and one on the lower curve). So, it fails the vertical line test.

Step3: Analyze Graph B

Graph B is a vertical line (e.g., \( x = 3 \) or some vertical line). A vertical line will intersect itself infinitely many times, so it fails the vertical line test (a vertical line is not a function of \( x \) since one \( x \) has multiple \( y \)-values).

Step4: Analyze Graph C

For Graph C, if we draw a vertical line (e.g., \( x = 2 \)), it will intersect the graph at two points (one on the upper curve and one on the lower curve). So, it fails the vertical line test.

Step5: Analyze Graph D

For Graph D, any vertical line we draw will intersect the graph at most once. Since it is a horizontal line, for every \( x \), there is exactly one \( y \)-value (in this case, \( y = 3 \) or whatever the horizontal line's \( y \)-value is). So, it passes the vertical line test.

Answer:

D (the graph labeled D, which is a horizontal line)