Graphing Exponential Functions

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Objective

SWBAT graph exponential functions showing intercepts and end behaviors, show key features of a graph, and review using function notation to evaluate functions for inputs in their domains.

Big Idea

Using tables to graph exponential functions, students explore exponential growth & decay while idenitfying properties such as domain, range, & asymptotes.

Lesson Author

Tiffany Dawdy

Phoenix, AZ

Grade Level

Twelfth grade

Subjects

Math

exponential function

exponential growth

Precalculus and Calculus

Standards

HSF-IF.A.2

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

HSF-IF.C.7e

Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

HSF-IF.C.8b

Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay.

HSF-LE.A.3

Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

MP1

Make sense of problems and persevere in solving them.

MP2

Reason abstractly and quantitatively.

MP3

Construct viable arguments and critique the reasoning of others.

MP5

Use appropriate tools strategically.

Warm-up

4 minutes

Vocabulary

1 minutes

Present page 5 of the flipchart to formally define exponential functions for students. They should add this to their Personal Dictionaries in their own words.

Graphing Exponentials

40 minutes

Domain and Range

Graphing Exponentials, video reflection, domain and range.MP4

Students should work through the Graphing Basic Exponential Functions handout. It is essential that all students work through question 12 to master the learning targets for today. Question 13 is more of an extension and those ideas will also be established later in this unit if students run out of time today. This activity could be completed individually by students or in teams. I will not be allowing the use of a graphing calculator for this activity.

As students are working though this activity I will be looking for them to demonstrate Mathematical Practice 6: attending to precision. I will specifically be checking each students graphs as I monitor the classroom to be sure that none of their graphs dip below the x-axis.

Another important practice I will be informally assessing as students work is their ability to apply Mathematical Practice 8: Look for and express regularity in repeated reasoning. I want to see students not only apply their exponent rules and tables to graph the functions, but be able to use the patterns and the their reasoning skills to conclude that exponential functions will never be equal to zero but will continue to get closer and closer to zero as x decreases in growth functions (or increases in a decay functions). Students understandings of this concept will be demonstrated in questions 1 and 4.

Closure

5 minutes

The closure questions today (pages 6-10 of the flipchart) assess students’ knowledge of identifying exponential growth and decay functions. Students should be able to match the graphs on the last two pages by simply using their knowledge of growth and decay functions.