Question

function f(x) = −2x + 6; f(x) is defined on the interval [−2,4].



A table of some inputs and outputs for the function is shown here:



x f(x)
–2 10
0 6
2 2




Which statement below is correct about the rate of change of the function over this interval?




The rate of change is greater from x = −2 to x = 0.


The rate of change is greater from x = 0 to x = 2.


The rate of change is greater from x = 2 to x = 4.


The rate of change does not change over the interval.

Answer 1

The rate of change does not change over the interval.

Reason: f(x) = −2x + 6 is linear with slope −2. For example,
- from x = −2 to 0: (6 − 10)/(0 − (−2)) = −4/2 = −2,
- from 0 to 2: (2 − 6)/(2 − 0) = −4/2 = −2,
- from 2 to 4: (−2 − 2)/(4 − 2) = −4/2 = −2.