Average Rate of Change Review

The given graph models Mr. Passwater’s distance from his home over time. Time, in hours, is the independent variable and the distance from home, in miles, is the dependent variable. Which of the following verbal descriptions would be appropriate for the given graph?

• Mr. Passwater leaves school and drives toward his house at a constant rate. Then, he stops to eat at a restaurant for a period of time to eat dinner. After eating dinner, Mr. Passwater leaves and drives until he reaches his house, driving at a constant rate that is faster than the rate he was driving when he first left school.

• Mr. Passwater leaves school and drives toward his house, increasing his speed as he drives. Then, he drives at a constant rate for a period of time. Finally, he increases his speed again and drives until he reaches his home.

• Mr. Passwater leaves his house and drives at a constant rate to a nearby restaurant. After stopping for a period of time to eat lunch, Mr. Passwater drives back to his home at a constant rate that is faster than his rate when driving to the restaurant.

• Mr. Passwater leaves his house and drives to a restaurant at a constant rate. Then, he stops to eat at a restaurant for a period of time to eat breakfast. After eating breakfast, Mr. Passwater leaves and drives until he reaches his school, driving at a constant rate that is faster than the rate he was driving when he first left his house.

f(x) = 2x² + 12x + 16
What is the average rate of change of f(x) on the interval [-3, -2].

• 2

• 1/2

• -2

• -1/2

Calculate the average rate of change from 20 to 40 minutes.

• -2 minutes per gallon

• -20 minutes per gallon

• -2 gallons per minute

• -20 gallons per minute

Which of the following scenarios would best represent the graph shown?

• Jackson ran to try and catch a bus at a stop near his house. He waited two minutes at the stop but realized he had missed the bus. So he slowly walked home.

• Wesley walked to the end of his driveway to get the newspaper and then turned to walk back inside at the same constant rate.

• Ben walked to a gas station close to his home to get a soda. He talked to some friends at the gas station for a few minutes. His mom called and told him to get home to do his Precal HW. The friend drove Ben back home. Luckily he got home faster in the car than when he walked.

• Jenny and her friend took the escalator to the 2nd story of the mall, shopped there for a while, and took the escalator back down.

The slope can also be called...

• the function

• the rate of change

• increasing

• positive

The Jamison family kept a log of the distance they traveled during a trip, as represented by the graph below. During which interval was their average speed the greatest?

• the first hour to the second hour

• the second hour to the fourth hour

• the sixth hour to the eighth hour

• the eighth hour to the tenth hour

Let s(x) give the total snowfall, in inches, x hours from the start of the snowstorm. Which expression can be used to find the average rate at which snow fell between 2 and 5 hours after the start of the snowstorm?

The graph of a function y = g(x) is shown. On which of the following intervals of x is g increasing at a decreasing rate?

• (-3, 1) U (4, ∞)

• (-1.4, 1) only

• (-1.4, 2.7)

• (-1.4, 1) U (4, ∞)

The graph of a smooth, continuous function g has a point at x = −7 where the rate of change of g changes from increasing to decreasing. Classify the point at x = −7 .

• g has an absolute minimum value at x = -7.

• g has an absolute maximum value at x = -7.

• g has an inflection point at x = -7.

• g has a local maximum at x = −7.

Selected values of a quadratic function m are given in the table. Find the value of z .

• 102

• 198

• 258

• 292