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All courses Algebra I · F-IF.2 20 of 76
Use function notation, evaluate functions on their domains, and interpret notation in context.

Evaluate a function at a given input by substitution

Problem
Evaluate \(f(x)=3x+2\) at \(x=4\).
Your answer
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Hint

Substitute 4 for x in f(x)=3x+2 before doing any arithmetic.

Function evaluation means replacing x with the given input and simplifying. For f(x)=3x+2, the input 4 must be used in the 3x term before adding 2.

Solution walkthrough

01

Identify the input and rule

\[f(x)~=~3x~+~2;~\text{input}~x~=~4\]

Evaluating the function means finding the output produced by the supplied input 4.

02

Substitute before calculating

\[f(4)~=~3(4)~+~2\]

Replace x by 4 inside the source rule, keeping the multiplication explicit.

03

Follow the operation order

\[3(4)~+~2~=~12~+~2~=~14\]

Multiply 3 by 4 first, then add the sourced constant 2.

04

Interpret and answer

\[f(4)~=~14;~\text{answer}~=~14\]

The function maps input 4 to output 14, so 14 is the requested value.

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Another way

  1. View the rule as double-checkable steps: triple 4 to get 12, then add 2 to get 14.

!

Common mistake

The input 4 is not the output, and adding before multiplying would change the source rule's operation order.

Solution walkthrough video