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

Study concepts, example questions & explanations for HiSET: Math

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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?

Possible Answers:

Correct answer:

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 .

Possible Answers:

Correct answer:

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 .

 

Possible Answers:

Correct answer:

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

.

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