HiSET: Math : Calculate and interpret rate of change over a specified interval

Example Questions

Example Question #1 : Calculate And Interpret Rate Of Change Over A Specified Interval

What is the slope of the line given by the following table?

Explanation:

Given two points

and

the formula for a slope is

.

Thus, since our given table is

we select two points, say

and

and use the slope formula to compute the slop.

Thus,

.

Hence, the slope of the line generated by the table is

.

Example Question #2 : Calculate And Interpret Rate Of Change Over A Specified Interval

Define .

Give the average rate of change of over the interval .

Explanation:

The average rate of change of a function over an interval is equal to

Setting , this is

Evaluate and by substitution:

,

the correct response.

Example Question #3 : Calculate And Interpret Rate Of Change Over A Specified Interval

Define .

Give the average rate of change of over the interval .

Explanation:

The average rate of change of a function over an interval is equal to

Setting , this is

Evaluate using the definition of for :

Evaluate  using the definition of for :

The average rate of change is therefore

.