A yard is equal in length to three feet. The function [tex]$f(x)$[/tex] takes a measurement in yards (as input) and returns a measurement in feet (as output).

[tex]
\begin{array}{clc}
& f(x)=3x \\
& & \\
\text {Input : } & & \text {Output} \\
\text {Yards} & \longrightarrow & \text {Feet} \\
1 & \longrightarrow \quad f(1)=3 \\
2 & \longrightarrow \quad f(2)=6 \\
12.2 & \longrightarrow & f(12.2)=? \\
\end{array}
[/tex]

What number will the function return if the input is 12.2?

A. 15.2
B. 14.2
C. 36.6
D. 36.2

Sure! Let's solve the problem step-by-step.

We are given a function [tex]$ f(x) $[/tex] which converts a measurement in yards to a measurement in feet. The relationship between yards and feet is given by the function:

[tex]\[ f(x) = 3x \][/tex]

This means that to convert a measurement in yards (input) to feet (output), we need to multiply the number of yards by 3.

We are asked to find the output when the input is 12.2 yards. To do this, we simply substitute [tex]$ x $[/tex] with 12.2 in the function [tex]$ f(x) $[/tex]:

[tex]\[ f(12.2) = 3 \times 12.2 \][/tex]

Now we perform the multiplication:

[tex]\[ 3 \times 12.2 = 36.6 \][/tex]

Thus:

[tex]\[ f(12.2) = 36.6 \][/tex]

So the function will return 36.6 feet when the input is 12.2 yards. The correct answer is:

C. 36.6