1. Graphing Exponential Functions Explain how to tell if an exponential function is growth or decay, and what an exponential growth and decay graph looks like.

2. Graphing Exponential Functions MM2A2. Students will explore exponential functions. b. Investigate and explain characteristics of exponential functions, including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, rates of change, and end behavior. (4.4, 4.5, 4.6) c. Graph functions as transformations of. (4.4, 4.5, 4.6)

3. Graphing Exponential Functions An exponential function has the form: (this is a little different than the book) If a > 0 and b > 1, then the function is an exponential growth function, and b is called the growth factor If a > 0 and 0 < b < 1, then the function is an exponential decay function, and b is called the decay factor What if a < 0? What if there is a negative in front of the x?

4. Graphing Exponential Functions An exponential function has the form: An asymptote is a line that a graph approaches more and more closely. The asymptote for this function will be y = k The graph will be shifted horizontally by h The end behavior of a function’s graph is the behavior of the graph as x approaches positive or negative infinity.

5. Graphing Exponential Functions Minimum steps to graph exponential functions: 1.Determine the asymptote by looking at the value of “k” – sketch it on the graph 2.Determine the general shape and end conditions by looking at the values of “a”, “b”, and the sign on the x. 3.Find the y-intercept by calculating and plotting x = 0 4.Determine the rough shape by calculating and plotting two more points (x = 1 may be good) 5.Smoothly draw the curve

6. Watch videos: http://www.onlinemathlearning.com/sketch- exponential-graph.html http://www.onlinemathlearning.com/sketch- exponential-graph.html Watch 1 st video from 3:30 introducing e Watch 2 nd video for negative transformations

7. Graphing Exponential Functions Determine the general shape, intervals of increase/decrease, asymptote, end behavior, domain, range, x and y intercepts, and average rate of change -1 < x < 2 of the following graphs?

8. Rate of Change What is rate of change? How do we calculate it? We can calculate the “average rate of change” for non-linear functions Find the average rate of change of the following functions for -2  x  2

9. Practice Page 122, # 1 – 12 all Page 127, # 1 – 6 all with explanations and 7 – 16 all.

10. Warm Up Find asymptote, determine general shape of curve, find y-intercept, graph, state the domain and range, end conditions, and find average rate of change 0 < x < 1

11. Given: f(x) = (2x + 7)(2x – 9), Find: Vertex – is it a minimum or maximum? AoS Domain Range x-intercepts y-intercept Intervals of increase/decrease End conditions Average rate of change from 0 < x < 2

12. Given the function: f(x) = 2(x - 4) 2 + 3, find: Vertex – is it a minimum or maximum? AoS Domain Range x-intercepts the solutions y-intercept Intervals of increase/decrease End conditions Average rate of change from 0 < x < 2 Write the function in standard form

13. Match the function to the graph

14. Given the function, find: Domain Range y-intercept Asymptote Zeros Intervals of increase/decrease End conditions Average rate of change from -2 < x < 2 Is function a growth or decay function?

15. Given the function, find: Domain Range y-intercept Asymptote Zeros Intervals of increase/decrease End conditions Average rate of change from -2 < x < 2 Is function a growth or decay function?

16. Given the function, find: Domain Range y-intercept Asymptote Zeros Intervals of increase/decrease End conditions Average rate of change from -2 < x < 2 Is function a growth or decay function?

17. Given the function, find: Domain Range y-intercept Asymptote Zeros Intervals of increase/decrease End conditions Average rate of change from -2 < x < 2 Is function a growth or decay function?

18. Compare and Contrast:

19. Practice Packet last two sheets - 4 problems