Interpreting and Sketching Qualitative Graphs
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Subject Area: Mathematics (B.E.S.T.) | Grade Level: 8
Lesson Length: 45 minutes
Keywords/Tags: Qualitative Graph, Function, Relationship, Increase, Decrease
Lesson Description: In this lesson, you will interpret graphs as qualitative functions. The relationships will always represent a function as no input of time can yield two different units. Students will apply their ability to identify functions, while describing functions in a real-world context. This will prepare students for the remainder of the unit where they will focus mainly on linear functions and briefly circle back to nonlinear functions.

  • Other 8.FGR.5: Describe the properties of functions to define, evaluate, and compare relationships, and use functions and graphs of functions to model and explain real phenomena.
Video : Qualitative Graphs
Instructions: Please watch the following video as many times as needed before starting to go through other lesson pages. Understanding the content of the video is very important since the lesson activities will be all about this video content.Please watch the following video as many times as needed before starting to go through other lesson pages. Understanding the content of the video is very important since the lesson activities will be all about this video content.")
Resources : Quizlet: Qualitative Graph
Instructions: Please see additional external resources below. Feel free visit each link to learn more about this lesson. https://quizlet.com/262270990/qualitative-graphs-flash-cards/
Quizlet: Qualitative Graph
Use this link to study and practice.
Quiz : Interpret and Sketch Graph
Instructions: Please complete this quiz by choosing the correct answer for each question. You can take this quiz as many times needed.
Question #1

1. A graph shows that as time passes, the temperature of a substance decreases. This is an example of

Question #2

2. A graph shows that as more hours are spent studying, the grades of a student improve. This is an example of a

Question #3

3. What does a flat line on a graph usually represent? 

Question #4
 4. Franco’s heart rate increases steadily as he does some warm-up exercises. He then maintains a steady heart rate for several minutes as he jogs. Finally, his heart rate slows down to normal with his cool-down walk. Sketch a graph to show Franco’s heart rate over time as he exercises. Tell whether the graph is continuous or discrete. 
Question #5
5. A person walks, gradually speeds up to a run, and then slows back down to a walk. Describe the relation between speed and time. 
Question #6
6. A person leaves home, drives through town, then on the highway, and finally stops at a rest area. Describe the relation between distance from home and time.  
Question #7

A theater will sell 500 tickets to a play if it charges $10 per ticket. Furthermore, every time it raises the price by one dollar, it will sell 50 fewer tickets because some people will think it too expensive. Which of the following functions t(d) represents the number of tickets the theater will sell if it charges d dollars per ticket?

Question #8

A taxi ride costs $4.25 for the first mile and $0.70 for each mile after the first. Which of the following functions c(d) gives the total cost (in dollars) of traveling d miles (assuming that d ≥ 1)?

Question #9

Exponential functions grow by equal factors over equal intervals. By what factor does the exponential function f(x)=3-2x grow by over every interval whose length is 3?

Question #10

A linear function can be used to convert a temperature from Fahrenheit to Celsius. For example, you can use it to convert 32oF to 0o C and 68o F to 20oC. Use this information to convert 104o F to Celsius.

Resources : Desmos: Graphing without Numbers
Instructions: Please see additional external resources below. Feel free visit each link to learn more about this lesson.
Video : Qualitative Graphs
Instructions: Please watch the following video as many times as needed before starting to go through other lesson pages. Understanding the content of the video is very important since the lesson activities will be all about this video content.
Resources : Qualitative Graph Notes and examples
Instructions: Please see additional external resources below. Feel free visit each link to learn more about this lesson.
Notes and Examples
Notes and additional examples
Resources : More Practice
Instructions: Please see additional external resources below. Feel free visit each link to learn more about this lesson.rnLearning Targets: rn1. Interpret characteristics of the qualitative graph of a function.rn2. Sketch a qualitative graph that matches a scenario