Function Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
Does the equation x2+y2=25x^2 + y^2 = 25 define yy as a function of xx?

Solution

  1. 1
    Solve for yy: y2=25−x2y^2 = 25 - x^2, so y=±25−x2y = \pm\sqrt{25 - x^2}.
  2. 2
    For example, when x=0x = 0, y=5y = 5 or y=−5y = -5. The input x=0x = 0 maps to two outputs.
  3. 3
    Since at least one input produces more than one output, yy is not a function of xx.

Answer

No, it is not a function.\text{No, it is not a function.}
A circle fails the vertical line test because most xx-values correspond to two yy-values. Recognizing common curve shapes helps you quickly identify which equations define functions.

About Function

A function is a rule that assigns to each input in the domain exactly one output in the codomain — every input maps to precisely one output, never two.

Learn more about Function →

More Function Examples

Example 1 easy

Determine whether the relation [formula] is a function.

Example 3 easy

Is the relation [formula] a function? Explain.

Example 4 hard

A graph passes through the points [formula], [formula], [formula], and [formula]. Does this graph re

Example 5 medium

Given [formula], find [formula] and determine if [formula] is a function.

← All Function Examples Function Concept