Algebra 2 average rate of change worksheet answer key

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Table of Contents Show

How do you find the average rate of change in Algebra 2?
What if the average rate of change is 0?
How do you find the average rate of change in a graph?

Directions: Read carefully. Choose the best answers.

When driving a car, an unsuspected hazard appears in the roadway. The table at the right shows the "total" stopping distance which is the sum of the "thinking" distance and the actual "braking" distance.
What is the average rate of change in the total stopping distance (feet/mph) between one car traveling 40 mph and one traveling 60 mph?

Speed (mph)	Total Stop Distance (ft.)
10	15
20	40
30	74
40	119
50	174
60	239

Total stopping distances calculated with "Car Stopping Distance Calculator" with "thinking" time as stated in
The Higheway Code.

x	g(x)
-3	-4
-2	3
-1	-6
0	2
1	-8

Which of the three functions shown above has the largest and smallest average rate of change on the interval [-3,0]?
Choose:

The table below shows the snowfall in a north-eastern city in inches for the first week in January.

Date

1/6

1/7

1/8

1/9

1/10

1/11

1/12

Snowfall (in.)

10"

18"

12"

24"

Find the average rate of change in the number of inches of snowfall from January 8 to January 11.

For which of the following two functions is the average rate of change constant?

When training for an event, a cross country runner used a FitBit to track his total distances traveled at half hour intervals.
a) What was the runner's average speed (mi/hr), during the first time interval?

Choose:

Reading	Time (hrs)	Distance (mi)
1	0.5	2.2
2	1	4.7
3	1.5	6.5
4	2	7.5
5	2.5	8.7

b) State between which two consecutive readings that the runner's average speed was the highest.
Choose:

c) State between which two consecutive readings that the runner's average speed was the lowest.
Choose:

Given: f (x) = e x
When examining equal consecutive intervals, which of the following statements is true regarding the average rate of change as x moves to the right?

Choose:

The graph of a straight line is shown below.
Which of the statements are true in relation to the statement:
"The average rate of change is ...."
(Check all that apply, and hit SUBMIT!)

An object is thrown upward from a height of 60 feet with an initial velocity of 48 feet per second. The height of the object t seconds after it is thrown is given by h (t) = -16t2 + 48t + 60.

a) What is the average velocity in the first two seconds after the object is thrown?
Choose:

b) What is the average velocity from t = 1 to t = 3?
Choose:

A rocket is 1.5 miles above the Earth in 20 seconds and is 8 miles above the Earth in 2 minutes. What is the rocket's rate of change in miles per second?

10.

Let f (x) = mx + b.
Find the average rate of change of f (x) between the points x = a and x = a + h.

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How do you find the average rate of change in Algebra 2?

To find the average rate of change, we divide the change in the output value by the change in the input value. The Greek letterΔ (delta) signifies the change in a quantity; we read the ratio as “delta-y over delta-x” or “the change iny divided by the change inx.

What if the average rate of change is 0?

When the average rate of change is zero, the sum of all possible positive slopes and negative slopes on the interval will be zero. The sum of the possible positive slopes cancels out the sum of the possible negative slopes. Finding average rate of change from a table.

How do you find the average rate of change in a graph?

The average rate of change formula is used to find the slope of a graphed function. To find the average rate of change, divide the change in y-values by the change in x-values. Finding the average rate of change is particularly useful for determining changes in measurable values like average speed or average velocity.