Given the function f(x) = 3x - 1, explain how to find the average rate of change between x = 1 and x = 4.

Step-by-step explanation:

f(1) = 3×1 - 1 = 2

f(4) = 3×4 - 1 = 12-1 = 11

so, the functional value changes 11-2=9 units on an x interval of 4-1=3 units length.

the average change rate is the total change across the x interval relative to the interval length.

that is

9/3 = 3

which is the slope (= the factor of x) in the line equation.

for a line its change rate for any point is the same constant. and that is therefore automatically also the average change rate across an interval of x values.

if the change rate would be different for different parts of the function, it would not be a straight line.

e

step-by-step explanation:

an equation by definition has to have two or more variables (x and 2 in this case)