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All courses Math III · F-IF.9 28 of 55
Compare functions represented algebraically, graphically, numerically, or verbally.

Compare the value of two functions at a given input from different representations

Problem
At x=2, which function has the greater value: f(x)=x²+1 or g, if the table shows g(2)=7?
Equation f of x equals x squared plus 1 beside a table row showing g of 2 equals 7. Open full size
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Hint

Evaluate both functions at the same input, \(x=2\), before comparing. Use the formula for \(f\) and the table value for \(g\).

For \(f(x)=x^2+1\), \(f(2)=2^2+1=5\). The table gives \(g(2)=7\), and \(7>5\), so \(g\) has the greater value.

Solution walkthrough

01

Evaluate f at x=2

\[f(2)~=~2^2~+~1\]

The question asks for a comparison at x=2, so substitute 2 into the formula for f.

02

Compute f(2)

\[f(2)~=~4~+~1~=~5\]

Square 2 first, then add 1 to get the output of f at the requested input.

03

Read g(2) from the table

\[g(2)~=~7\]

The question gives the table value directly, so no formula for g is needed.

04

Compare the outputs

\[7~>~5\]

Compare the two outputs found at the same input, x=2.

05

State the comparison

\[f(2)=5~\text{and}~g(2)=7,~\text{so}~g~\text{is}~\text{greater}.\]

Since g(2) is larger than f(2), g has the greater value at x=2.

+

Another way

  1. Check the two outputs on a number line: 7 is to the right of 5, so 7 is greater.

!

Common mistake

A common mistake is comparing values at different inputs instead of using x=2 for both functions. The question fixes the input at x=2, so both outputs must be evaluated there before comparing.

Equation and table comparison showing f of 2 equals 5 and g of 2 equals 7, so g is greater.
At x = 2, g is greater: 7 > 5.