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