Question

(a) Is the average rate of change of a function between $x=a$and $x=b$the slope of the secant line through $\left(a,f\left(a\right)\right)$and $\left(b,f\left(b\right)\right)$?

(b) Is the average rate of change of a linear function the same for all intervals?

Short answer

(a) Yes

(b) Yes

Step-by-step solution

Given Information

(a) The average rate of change of a function between $x=a$and $x=b$the slope of the secant line through $\left(a,f(a\right)$and $\left(b,f\left(b\right)\right)$.

(b) The average rate of change is the same in all intervals.

Part (a) Step 1: Yes/No

The statement is correct because the rate of change of a function between two points is the secant of a line.

Part (b) Step 1: Yes/No

The average rate of change of a function is constant for a line for all intervals.