Which of the following equations is NOT a function?

Question

Which of the following equations is not a function?

a) y=x^2-x-1

b) y= √x-1

c) y= x^2-1

d) y^2=x-1

 

Answer 1

The answer is D.

 

A graph of the equation gives a horizontal parabola.   A vertical line can cut the graph in two places, and accordingly, the graph fails the vertical line test.

 

Or viewed another way, a single value of x, for example, 17, corresponds to two values of y (4, and -4).  For a function, we must have a single of Y for any x value in the domain.