Curriculum / Math / 8th Grade / Unit 4: Functions / Lesson 11
Math
Unit 4
8th Grade
Lesson 11 of 12
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Describe functions by analyzing graphs. Identify intervals of increasing, decreasing, linear, or nonlinear activity.
The core standards covered in this lesson
8.F.B.5 — Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
Lessons 11 and 12 focus on graphical representations of functions and understanding them qualitatively. In Lesson 11, students analyze the structural appearance of graphs to understand and describe how the behavior of the function changes (MP.7). In Lesson 12, students sketch graphs when given descriptions.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
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.
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.
Distance, accessed on Oct. 27, 2017, 10:54 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
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.
Bike Race, accessed on Oct. 27, 2017, 10:55 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
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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.
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.
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
Lesson 10
Lesson 12
Topic A: Defining Functions
Define and identify functions.
8.F.A.1
Use function language to describe functions. Identify function rules.
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Topic B: Representing and Interpreting Functions
Identify properties of functions represented in tables, equations, and verbal descriptions. Evaluate functions.
8.F.A.1 8.F.A.2 8.F.B.4
Represent functions with equations.
8.F.A.1 8.F.B.4
Read inputs and outputs in graphs of functions. Determine if graphs are functions.
Identify properties of functions represented in graphs.
Topic C: Comparing Functions
Define and graph linear and nonlinear functions.
8.F.A.3
Determine if functions are linear or nonlinear when represented as tables, graphs, and equations.
8.F.A.1 8.F.A.3
Compare functions represented in different ways (Part 1).
8.F.A.2
Compare functions represented in different ways (Part 2).
Topic D: Describing and Drawing Graphs of Functions
8.F.B.5
Sketch graphs of functions given qualitative descriptions of the relationship.
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