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All courses Math I · F-BF.1.b 16 of 59
Combine standard functions using arithmetic operations to build models.

Add two functions and interpret the combined output

Problem
For x items, f(x)=3x+10 dollars is supplier A's cost and g(x)=2x+5 dollars is supplier B's cost.
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Hint

Add the two function rules term by term because the context combines two costs.

When two modeled quantities happen together, their total is often found by addition.

Solution walkthrough

01

Write the two functions

\[f(x)~=~3x~+~10,~g(x)~=~2x~+~5\]

Start with the two expressions that model the separate costs.

02

Add the expressions

\[(f+g)(x)~=~(3x~+~10)~+~(2x~+~5)~=~5x~+~15\]

Add like terms because the context asks for the total from both cost sources.

03

State the combined function

\[(f+g)(x)~=~5x~+~15\]

This is the rule for the sum of the two functions.

04

Interpret the result

\[\text{rule}~=~(f+g)(x)=5x+15;~\text{summed}~\text{quantities}~=~\text{supplier}~A~\text{cost}~+~\text{supplier}~B~\text{cost};~\text{output}~=~\text{combined}~\text{cost}~\text{for}~x~\text{items};~\text{unit}~=~\text{dollars}\]

The combined function gives the total cost when both sources are included for x items.

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Another way

  1. You can think of the model as cost from source one plus cost from source two.

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Common mistake

A common mistake is to multiply the functions just because two rules are shown. Here the context asks for a total, so the functions should be added.