Fishtank Learning
8th Grade Math
Unit 4: Functions
Lesson 11
Objective
Describe functions by analyzing graphs. Identify intervals of increasing, decreasing, linear, or nonlinear activity.
Warm Up
Watch the video of a subway arriving at a station.
What do you notice? What do you wonder?
Anchor Problems - Problem 1
Use the graph of the function below to answer the questions that follow.
a. Name an interval of $$x$$ where the function is linear.
b. Name an interval of $$x $$ where the function is increasing.
c. Name an interval of $$x$$ where the function is decreasing linearly.
d. In what interval of $$x$$ is the function increasing at its greatest rate?
e. Explain what is happening in the interval where $$x$$ is between 2 and 4.
Anchor Problems - Problem 2
Below are two graphs that look the same. Note that the first graph shows the distance of a car from home as a function of time, and the second graph shows the speed of a different car as a function of time.
Describe what someone who observes each car’s movement would see in each case.
a. 
b. 
Anchor Problems - Problem 3
Antonio and Juan are in a 4-mile bike race. The graph below shows the distance of each racer (in miles) as a function of time (in minutes).
a. Who wins the race? How do you know?
b. Imagine you were watching the race and had to announce it over the radio; write a little story describing the race.
Problem Set
Target Task - Problem 1
The graph below shows how the altitude of a flight from Boston to Chicago changes over time. Use the graph to answer the following questions.
a. Cruising altitude is the sustained, consistent, altitude that planes maintain during flight between take-off and landing. Between what two values of $$x$$ was this flight at cruising altitude?
b. How long was the plane in the air?
c. Describe an interval of $$x$$ where the plane’s altitude was decreasing.
d. Describe an interval of $$x$$ where the plane’s altitude was increasing.
Target Task - Problem 2
Refer to the graph in Target Task problem 1. Which of the following must be true about the interval between $$x=0$$ and $$x=15$$? Choose all that apply.
A. The plane did not move.
B. The plane was on the ground.
C. The plane's altitude was constant.
D. The plane's altitude was 0.
E. The plane's altitude was 15.