Function Math Example 5

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Example 5

medium
Given f(x)=2x2−3x+1f(x) = 2x^2 - 3x + 1, find f(4)f(4) and determine if g={(1,2),(3,4),(1,5)}g = \{(1,2), (3,4), (1,5)\} is a function.

Solution

  1. 1
    Evaluate f(4)f(4): substitute x=4x = 4 into f(x)=2x2−3x+1f(x) = 2x^2 - 3x + 1. We get f(4)=2(4)2−3(4)+1=2(16)−12+1=32−12+1=21f(4) = 2(4)^2 - 3(4) + 1 = 2(16) - 12 + 1 = 32 - 12 + 1 = 21.
  2. 2
    For g={(1,2),(3,4),(1,5)}g = \{(1,2), (3,4), (1,5)\}, check whether each input maps to exactly one output.
  3. 3
    The input x=1x = 1 maps to both y=2y = 2 and y=5y = 5. Since one input has two different outputs, gg is NOT a function.

Answer

f(4)=21;g is not a functionf(4) = 21; \quad g \text{ is not a function}
A function must assign exactly one output to each input. Evaluating a function at a point means substituting the input value everywhere the variable appears. A set of ordered pairs fails to be a function if any input appears with more than one output.

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.

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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 4 hard

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

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