High School

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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]

\[
\begin{array}{ll}
\text{Input:} & \text{Output:} \\
\text{Yards} & \text{Feet}
\end{array}
\]

\[
\begin{array}{rlr}
1 & \longrightarrow \quad f(1) = 3 \\
2 & \longrightarrow \quad f(2) = 6 \\
12.2 & \longrightarrow \quad f(12.2) = \, ?
\end{array}
\]

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

A. 36.2
B. 36.6
C. 14.2

Answer :

To solve the problem of converting yards into feet, we need to use the relationship that 1 yard is equal to 3 feet. Therefore, when we are given an input in yards, we can determine the output in feet by multiplying the number of yards by 3.

Let's go through the steps:

1. Understand the Conversion:
- We have a function [tex]\( f(x) = 3x \)[/tex], which means for any given number of yards ([tex]\( x \)[/tex]), the function will return three times that number in feet.

2. Identify the Input:
- The input in this case is 12.2 yards.

3. Apply the Conversion:
- Use the function: [tex]\( f(12.2) = 3 \times 12.2 \)[/tex].

4. Calculate:
- [tex]\( 3 \times 12.2 \)[/tex] equals to 36.6 feet.

Therefore, when the input is 12.2 yards, the function will output 36.6 feet.

Given the choices:
- A. 36.2
- B. 36.6
- C. 14.2

The correct answer is B. 36.6. This is the number of feet corresponding to 12.2 yards.

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