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

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 $\boxed{2}$.

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