Questions: This table shows input and output values for a linear function f (x). What is the positive difference of outputs for any two inputs that are four values apart? Enter your answer in the box. x f(x) -3 -1.5 -2 -1 -1 -0.5 0 0 1 0.5 2 1.5 3

This table shows input and output values for a linear function f (x).

What is the positive difference of outputs for any two inputs that are four values apart?

Enter your answer in the box.

x f(x)
-3 -1.5
-2 -1
-1 -0.5
0 0
1 0.5
2 1.5
3

Transcript text: This table shows input and output values for a linear function f (x). What is the positive difference of outputs for any two inputs that are four values apart? Enter your answer in the box. $\square$ \begin{tabular}{|l|l|} \hline$x$ & $f(x)$ \\ \hline-3 & -1.5 \\ \hline-2 & -1 \\ \hline-1 & -0.5 \\ \hline 0 & 0 \\ \hline 1 & 0.5 \\ \hline 2 & 1.5 \\ \hline 3 & \\ \hline \end{tabular}

Solution

Find the positive difference of outputs for any two inputs that are four values apart.

Identify the linear function $ f(x) $.

From the table, observe the relationship between $ x $ and $ f(x) $. The outputs increase by 0.5 for every increase of 1 in $ x $. This indicates the slope $ m = 0.5 $. The function can be written as $ f(x) = 0.5x $.

Verify the function with given values.

For $ x = -3 $, $ f(-3) = 0.5(-3) = -1.5 $.
For $ x = -2 $, $ f(-2) = 0.5(-2) = -1 $.
For $ x = 1 $, $ f(1) = 0.5(1) = 0.5 $.
The function $ f(x) = 0.5x $ matches the table.

Calculate the outputs for two inputs that are four values apart.

Choose $ x = 0 $ and $ x = 4 $.
For $ x = 0 $, $ f(0) = 0.5(0) = 0 $.
For $ x = 4 $, $ f(4) = 0.5(4) = 2 $.

Find the positive difference of outputs.

The positive difference is $ |f(4) - f(0)| = |2 - 0| = 2 $.

The positive difference of outputs for any two inputs that are four values apart is $ \boxed{2} $.

Was this solution helpful?