Lesson 3: 2-3 Extrema and End Behavior

How do you find the end behavior of a function?
Is there a difference between how you find the end behavior of a linear function and of a nonlinear functions? Explain
How do you find the number of extrema of a function by looking at its graph?

end behavior
relative maximum
relative minimum
turning points
extrema

F.IF.4 For a function that models a relationship between two quantities, interpret key features of expressions, graphs and tables in terms of the quantities, and sketch graphs showing key features given a description of the relationship.
F.IF.7c Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

tbd

Studying the key features of a graph can give you insight into trends in the data represented by the function. Key features to look for include relative maximum and relative minimum points, zeros, the y-intercept, and the end behavior of the function as the values of x increase or decrease without bound

The relationship between the speed of a car in mph and the distance in feet it takes for the car to stop after braking can be modeled by the graph of a nonlinear function. Do you think the speed of the car in mph and the braking distance can have unlimited values?

Remember that some graphs have no extrema, for example having not relative maximums or minimums

Have students look for real world graphs on the internet that have extrema. For example, stock prices show extrema

Use McGraw Hill resources

Use McGraw Hill resources