Lesson 6: 1-8 Interpreting Graphs of Functions

How can you find the intercepts of a graph?

If x measures time in hours and y measures distance from New York in miles, interpret the y-intercept.

What does it mean for a graph to have symmetry?

intercept
x-intercept
y-intercept
line symmetry
positive
negative
increasing
decreasing
extrema
relative maximum
relative minimum
end behavior

F.IF.4
B. Interpret functions that arise in applications in terms of the context
4. HSF-IF.B.4
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

F.IF.5
5. HSF-IF.B.5
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.

F.IF.9
9. HSF-IF.C.9
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.

Chapter 1A (1-1 - 1-4) (Skip 1-3) 1B (1-6-1-8 skip end behavior) (Skip 1-5)

To interpret a graph, estimate and interpret key features of the graph. These include the intercepts, intervals where the function is increasing or decreasing, intervals where the function is positive or negative, extrema, symmetry, and end behavior.

Why would a linear function not model the sale of video games well?

Describe some points or areas on a graph of video game sales that might be of more interest to someone in the video game industry than other points.

If students are having trouble interpreting key features of graphs, then have students work together discussing examples in this lesson. You may also want them to complete some exercises cooperatively.

Extension Have pairs of students challenge each other to draw graphs with given key features. One student draws a graph without showing it to the other and describes its key features. The second student should draw a graph that fits the description. Discuss similarities and differences in the graphs and whether both graphs fit the description. Then switch roles and repeat.

Exercises 1-4

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