Which of the graphs below represent y as a function of x?
(a)
(b)

A) both (a) and (b)
B) neither (a) nor (b)
C) only (b)
D) only (a)

Question

Which of the graphs below represent y as a function of x? ​
(a)
​  (b)
​  ​
A) both (a) and (b) 
B) neither (a) nor (b) 
C) only (b) 
D) only (a)

Quizplus · Accepted Answer

In order for y to be a function of x, there can only be one y-value for each x-value. In graph (a), there are some x-values that have multiple y-values. For example, when x=1, there are two possible y-values: y=2 and y=-2. Therefore, graph (a) does not represent y as a function of x.

Graph (b), on the other hand, passes the vertical line test, meaning that for each x-value, there is only one corresponding y-value. Thus, graph (b) represents y as a function of x.

Which of the Graphs Below Represent Y as a Function