College

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

[tex]\[

\begin{array}{ccc}

\text{Input: Yards} & \longrightarrow & \text{Output: Feet} \\

1 & \longrightarrow & f(1) = 3 \\

2 & \longrightarrow & f(2) = 6 \\

12.2 & \longrightarrow & f(12.2) = ?? \\

\end{array}

\][/tex]

What number will the function return if the input is [tex]12.2[/tex]?

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

Answer :

To solve this problem, we need to convert the measurement provided in yards to the equivalent measurement in feet.

The function we're dealing with is [tex]\( f(x) = 3x \)[/tex], where [tex]\( x \)[/tex] is the input in yards, and the function returns the output in feet. This function simply multiplies the input by 3 because there are 3 feet in a yard.

We're given an input of 12.2 yards and need to find out the equivalent in feet. Here's how you can think about it step-by-step:

1. Understand the Relationship: We know that 1 yard is equal to 3 feet. Hence, the function [tex]\( f(x) = 3x \)[/tex] helps us convert yards to feet.

2. Substitute the Input: Take the given input of 12.2 yards and substitute it into the function. This means we need to compute:
[tex]\[
f(12.2) = 3 \times 12.2
\][/tex]

3. Perform the Multiplication: Multiply 3 by 12.2:
[tex]\[
3 \times 12.2 = 36.6
\][/tex]

4. Determine the Output: The function [tex]\( f(x) \)[/tex] will return 36.6 feet when the input is 12.2 yards.

Hence, if the input is 12.2, the function will return 36.6. Therefore, the correct answer is:

B. 36.6

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