Question

1. which equation does not represent a function?

a. $y = \sqrt{x}$
b. $y = x + 1$
c. $y^2 = x$
d. $y = x^2$

Explanation:

Step1: Recall function definition

A function assigns exactly one output $y$ for each input $x$ in its domain.

Step2: Test option a

For $y=\sqrt{x}$, each valid $x\geq0$ gives one non-negative $y$. This is a function.

Step3: Test option b

For $y=x+1$, every $x$ gives exactly one $y$. This is a function.

Step4: Test option c

For $y^2=x$, take $x=4$: $y=2$ or $y=-2$. One $x$ gives two $y$-values. This is not a function.

Step5: Test option d

For $y=x^2$, every $x$ gives exactly one $y$. This is a function.

Answer:

c. $y^2 = x$