Answer:
x squared = y
Step-by-step explanation:
Functions
Things can get more complicated, but based on the examples given, for an equation to be a function of x, it must have a single y, where the y is not raised to a power.
Option 1: x=5
This equation doesn't have a y, so it isn't a function of x.
Option 2: x = y squared + 9
This equation has y raised to a power, so it isn't a function of x
Option 3: x squared = y
This equation has a y, and the y isn't raised to a power. This is a function of x.
Option 4: x squared = y squared + 16
This equation has y raised to a power, so it isn't a function of x
Determining functions graphically
If the equations are graphed, the graphs must pass a vertical line test (a vertical line drawn anywhere should not intersect the graph more than once).
Option 1: x=5
x=5 represents a vertical line, so it fails the vertical line test (the vertical line would overlap and intersect it infinitely many times).
Option 2: x = y squared + 9
x = y squared + 9 is a sideways parabola. A vertical line will cross it twice in several places
Option 3: x squared = y
x squared = y is a parabola that opens upward. It will pass the vertical line test
Option 4: x squared = y squared + 16
x squared = y squared + 16 is a hyperbola (fancy graph shape) that won't pass the vertical line test.
