4.06-4.09 Analyzing and Creating Graphs of Functions

This graph represents Andre’s distance from his bicycle as he walks in a park.

Decide whether the following statements are true or false.

a. The graph has multiple horizontal intercepts.

b. A horizontal intercept of the graph represents the time when Andre was with his bike.

c. A minimum of the graph is (17, 1).

d. The graph has two maximums.

e. About 21 seconds after he left his bike, he was the farthest away from it, at about 8.3 feet

• False

  True

  False

  False

  True

• True

  True

  False

  True

  True

• True

  True

  False

  False

  True

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The graph represents the temperature in degrees Fahrenheit as a function of time.

Complete the following to tell the story of the temperature throughout the day.

The day started out _______ in the morning but _______ quickly by lunchtime. It reached the warmest temperature around _____ p.m. and then cooled down slowly. After sunset, the temperature _______ more quickly. By 9 p.m., it reached the same point as at the start of the day, which is the _______ temperature up to that point of the day.

​

• cold

  warmed up

  3

  decreased

  coldest

• warm

  cooled down

  7

  increased

  warmest

• cold

  warmed up

  7

  increased

  warmest

• warm

  cooled down

  3

  decreased

  coldest

Match each feature of the situation with a corresponding statement in function notation.

• 
• 
• 

The height, in feet, of a squirrel running up and down a tree is a function of time, in seconds. Here are statements describing the squirrel’s movement during four intervals of time. Match each description with a statement about the average rate of change of the function for that interval.

• 
• 
• 

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The percent of voters between the ages of 18 and 29 that participated in each United States presidential election between the years 1988 to 2016 are shown in the table.

The function P gives the percent of voters between 18 and 29 years old that participated in the election in year t.

Complete the following to indicate the average rate of change for P between 1992 and 2000.

P(t) ______ per year between 1992 and 2000.

Between which two values of t does the function have a negative average rate of change? 

Between which two values of t does the function have a positive average rate of change? 

​

• decreased 4.1%

  t = 1988 and t = 2016

  t = 2008 and t = 2012

• decreased 4.1%

  t = 2008 and t = 2012

  t = 1988 and t = 2016

• decreased 1.025%

  t = 2008 and t = 2012

  t = 1988 and t = 2016

• decreased 1.025%

  t = 1988 and t = 2016

  t = 2008 and t = 2012

Here are descriptions of four situations in which the volume of water in a tank is a function of time.

Match each description to a corresponding graph.

A. An empty 20-gallon water tank is filled at a constant rate for 3 minutes until it is half full. Then, it is emptied at a constant rate for 3 minutes.

B. A full 10-gallon water tank is drained for 30 seconds, until it is half full. Afterwards, it gets refilled.

C. A 2,000-gallon water tank starts out empty. It is being filled for 5 hours, slowly at first, and faster later.

D. An empty 100-gallon water tank is filled in 50 minutes. Then, a dog jumps in and splashes around for 10 minutes, letting 7 gallons of water out. The tank is refilled afterwards.

• Graph 3

  Graph 1

  Graph 2

  Graph 4

• Graph 3

  Graph 1

  Graph 4

  Graph 2

• Graph 1

  Graph 3

  Graph 2

  Graph 4

• Graph 1

  Graph 3

  Graph 4

  Graph 2

Clare described her morning at school yesterday: “I entered the school on the first floor, then walked up to the third floor and stayed for my class for an hour. Afterward, I had an hour-long class in the basement, and after that, I went back to the ground level and sat outside to eat my lunch."

Which is a possible graph of her height from the ground floor as a function of time?

• Graph A

• Graph B

 Functions R and D give the height, in feet, of a toy rocket and a drone, t seconds after they are released. Here are the graphs of R (for the rocket) and D (for the drone).

Which correctly represents each statement in function notation?

a. At 3 seconds, the toy rocket is higher than the drone.

b. At the start, the toy rocket is 25 feet above the drone.

• R(3) > D(3)

  R(0) = D(0)

• R(3) > D(3)

  R(0) = D(0) + 25

• R(3) < D(3)

  R(0) = D(0) + 25

• R(3) < D(3)

  R(0) = D(0)

Here are two graphs representing functions f and g.

Select all statements that are true about functions f and g.

(there are 3)

• f(0)>g(0)

• There are two values of x where f(x)=g(x).

• f(-1)<g(-1)

• f(-3)>g(4)

​

 The three graphs represent the progress of three runners in a 400-meter race. The solid line represents runner A. The dotted line represents runner B. The dashed line represents runner C.

a. One runner ran at a constant rate throughout the race. Which one?

b. A second runner stopped running for a while. Which one?

c. Which runner finished second?

d. Who won the race?

​

• Runner A

  Runner C

  Runner B

  Runner C

• Runner B

  Runner A

  Runner B

  Runner C

• Runner C

  Runner A

  Runner B

  Runner C