## Unit 4

Analyzing Exponential Functions

**Unit Description**

In this unit, students will construct and analyze the graph of an exponential function to explain a contextual situation for which the graph serves as a model; compare exponential with linear and quadratic functions. Students will compare exponential with linear and quadratic functions.

Building on the previous unit (Unit 5) of this course, the students will explore exponential functions. Students will explore the effects of vertical shifts and stretches on key characteristics of the functions including domain, range, intercepts, average rate of change, intervals where the function is increasing or decreasing, positive or negative; relative maximums and minimums; symmetries; asymptotes; and end behaviors. These explorations will be done using interactive technology.

Building on the previous unit (Unit 5) of this course, the students will explore exponential functions. Students will explore the effects of vertical shifts and stretches on key characteristics of the functions including domain, range, intercepts, average rate of change, intervals where the function is increasing or decreasing, positive or negative; relative maximums and minimums; symmetries; asymptotes; and end behaviors. These explorations will be done using interactive technology.

**Learning Targets**

- I can identify and define geometric sequences
- I can create exponential functions using function notation
- Using the formula for an explicit or recursive formula, I can determine the next “n” terms of a sequence
- I can convert geometric sequences from recursive to explicit form and vice versa
- I can compare geometric sequences and arithmetic sequences in a variety of ways
- I can sketch a graph of an exponential function showing key features including domain, range, intercepts, average rate of change, intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; asymptotes; end behavior.
- Given a graph, table, or a function, I can determine the appropriate domain and range for the function
- I can estimate the average rate of change from an exponential graph
- I can express characteristics in interval notation and set-builder notation using inequalities
- I can identify the effect of transformations to the parent exponential function
- I can compare key characteristics of functions given different representations (algebraically, graphically, in tables, and by verbal descriptions)

**Textbook Connections**

__Module 9__

Lesson 2- Transformations of Exponential Functions: Students identify the effects of transformations of the graphs of exponential functions.

Lesson 5- Geometric Sequences: Students write and graph equations of geometric sequences.

Lesson 6- Recursive Formulas: Students write and graph equations of geometric sequences.

**IXL Skills**

P.1 Identify arithmetic and geometric sequences

P.10 Convert a recursive formula to an explicit formula

P.11 Convert an explicit formula to a recursive formula

P.12 Number sequences: mixed review

P.10 Convert a recursive formula to an explicit formula

P.11 Convert an explicit formula to a recursive formula

P.12 Number sequences: mixed review