Function Math Example 4

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

Example 4

hard
A graph passes through the points (1,2)(1, 2), (2,5)(2, 5), (3,5)(3, 5), and (1,7)(1, 7). Does this graph represent a function? Explain using the vertical line test.

Solution

  1. 1
    The vertical line test says: if any vertical line crosses the graph more than once, it is NOT a function.
  2. 2
    At x=1x = 1, there are two outputs: y=2y = 2 and y=7y = 7. A vertical line at x=1x = 1 would hit two points.
  3. 3
    Since one input (x=1x = 1) maps to two different outputs, this relation is not a function.

Answer

Not a function — the input x=1x = 1 gives two different outputs (22 and 77), failing the vertical line test.
A function assigns exactly one output to each input. The vertical line test is the graphical version of this rule: no vertical line should cross the graph more than once.

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 2 medium

Does the equation [formula] define [formula] as a function of [formula]?

Example 3 easy

Is the relation [formula] a function? Explain.

Example 5 medium

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

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