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All courses Algebra II · F-IF.9 35 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 \(x~=~2\), evaluate \(f(x)~=~x^2~+~1\) and use the table value \(g(2)~=~7\). Compare the \(\text{two}~\text{function}~\text{values}\).
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 the equation-defined function

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

The requested input is x=2. Substituting it into f(x)=x squared plus 1 gives the exact value 5.

02

Read the table-defined value

\[\text{table}~\text{row}~x=2~->~g(2)=7\]

The inspected prompt table pairs input 2 with output 7. This value is read from the table rather than computed with f's equation.

03

Compare at the same input

\[\text{Function}~g~\text{has}~\text{the}~\text{greater}~\text{value}~\text{because}~f(2)=2^2+1=5~\text{and}~\text{the}~\text{table}~\text{shows}~g(2)=7.\]

Both values refer to x=2, and 7 is greater than 5, so g has the larger function value.

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Another way

  1. Write the ordered pairs (2,5) for f and (2,7) for g, then compare their y-coordinates.

!

Common mistake

Do not substitute 2 into the table output or apply f's formula to g. Each representation supplies its own function value at the shared input.

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.

Solution walkthrough video