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}
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Solution

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

Identify the linear function f(x) f(x) .

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

Verify the function with given values.

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

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

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

Find the positive difference of outputs.

The positive difference is f(4)f(0)=20=2 |f(4) - f(0)| = |2 - 0| = 2 .

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

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

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