Question

This table shows the 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?

x: 3 2 1 0 1 2 3
f(x): −1.5 −1 −0.5 0 0.5 1 1.5

Answer 1

For the linear function f(x), the output increases by 0.5 for each 1 unit increase in x. Hence, for any two inputs four units apart, the positive difference of outputs is 0.5 * 4 = 2.

Step-by-step explanation:

The student's question asks about finding the positive difference of outputs for a given linear function f(x) for any two inputs that are four units apart. By examining the table, we can see that for every increase of 1 in x, the output f(x) increases by 0.5. This implies a constant rate of change which is a hallmark of linear functions.

The difference in outputs for two x-values that are four units apart can be determined by multiplying the rate of change by the difference in the x-values. Since the rate of change is 0.5, and the difference in x is 4, the positive difference in outputs will be 0.5 * 4 = 2.

Therefore, for this linear function, the positive difference of outputs for any two inputs that are four units apart is consistently 2. This illustrates the consistent rate at which the output of a linear function changes in relation to its input.