Question

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 three values apart?

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

Answer 1

The positive difference of outputs for any two inputs that are three units apart in a linear function is equal to the slope multiplied by the input difference, which in this case is 1.5.

Step-by-step explanation:

When looking at a linear function like f(x) and given a set of input (x) and output (f(x)) values, the rate of change between any two points is constant. This rate is known as the slope of the line. The question asks for the positive difference of outputs for any two inputs that are three values apart. To find this, we calculate the change in the output values when the input values increase by three units.

Based on the information provided, as the input increases by one, the output increases by 0.5. Therefore, for an increase of three units in input, the output will increase by 0.5 * 3 = 1.5 units. The positive difference of outputs for any two inputs that are three units apart will consistently be 1.5.