Possible Functions

If $y$ is a function of $x$ then there is exactly one value of $y$ for each $x$ .

A) $y = 2x - 5$ : This has one value of $y$ for all $-10 \leq x \leq 10$ .

B) $x^2 + y^2 = 1$ : Making $y$ the subject of the equation, we have $y = \pm \sqrt{1 - x^2}$ , thus for $x = 0$ we have $y = \pm 1$ . Hence this relation is not a function.

C) $x = 20 - \frac{2}{y}$ : Making $y$ the subject of the equation, we have $y = \frac {2}{20-x}$ and this has one value of $y$ for all $-10 \leq x \leq 10$ .

D) $y = \sqrt{10 - x^2}$ : When $x> \sqrt{10}$ , $y$ is not real valued, hence this relation is not a function on the domain $-10 \leq x \leq 10$ .

E) $y = 2x^2 - 3x + 4$ : This has one value of $y$ for all $-10 \leq x \leq 10$ .

F) $y = |x|$ : This has one value of $y$ for all $-10 \leq x \leq 10$ .

Therefore $4$ of the $6$ relations are functions of $x$ in the domain $-10 \leq x \leq 10$ .