Question

Which equation is a function of x?
A. x=5
B. x=y2+9
C. x2=y
D. x2=y2+16

Answer 1

A function is a process or a relation that associates each element x of a set X to a single element y of another set Y.

A. The equation
`x=5` represents vertical line. This is not a function, because one element x=5 is associated to all (not one) elements of
`y\in (-\infty,\infty).`

B. The equation
`x=y^2+9` represents parabola that goes in positive x-direction. This is not a function, because each
`x>9` is associated to two different y. For examlpe, when x=10, then
`y_1=1,\ y_2=-1.`

C. The equation
`y=x^2` represents parabola that goes in positive y-direction. This is the function, because for each x is associated only one y.

D. The equation
`x^2=y^2+16` represents hyperbola. This is not a function, because for one x there are two different possible y.

Answer: correct choice is C