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.

Step2: Analyze Graph A

For Graph A, if we draw a vertical line (e.g., at \( x = - 3 \)), it will intersect the graph at two points (upper and lower parts of the ellipse - like shape). So, it fails the vertical line test.

Step3: Analyze Graph B

Graph B is a vertical line ( \( x = 3 \) ). A vertical line by itself fails the vertical line test because it has infinitely many \( y \)-values for a single \( x \)-value.

Step4: Analyze Graph C

For Graph C, similar to Graph A, a vertical line (e.g., at \( x = 2 \)) will intersect the graph at two points (upper and lower parts of the ellipse - like shape). So, it fails the vertical line test.

Step5: Analyze Graph D

Graph D is a horizontal line ( \( y = 3 \) ). For any vertical line, it will intersect the graph at most once (since it's horizontal, each \( x \) has exactly one \( y \)-value, \( y = 3 \)). So, it passes the vertical line test.

Answer:

D (the graph labeled D, which is the horizontal line \( y = 3 \))