Question

Which of the following expressions represents a function?

y = x2
{(9, 2), (4, –2), (5, 3), (9, –4)}
x = –3
x2 = 25 − y2

Answer 1

A function is a relation where there is only one y-value for each x-value. According to this definition, the only given expression that represents a function is y = x^2

Answer 2

y=x²

Explanation:

Function is a map from a non-empty set A to a non-empty set B such that corresponding to each point of A there exist a unique image of it in B.

y=x² corresponding to each x there exist a unique image i.e. value of y

Hence, it is a function.

{(9, 2), (4, –2), (5, 3), (9, –4)}

since, for x=9 there exists two images 2 and -4

Hence, it is not a function.

x=-3

it is not a function

x² = 25 − y²

for x=0 y can be 5 or -5

i.e. there exists two images of a function under x=0

Hence, it is not a function.