1 Factoring Practice (5 questions)

2 Factoring Practice (Answers)

Exponential Functions and Their Graphs Sections 7-1,2,3

4 Objectives I can recognize growth or decay exponential equations I can graph exponential growth and decay parent functions

5 The exponential function f with base b is defined by f(x) = b x where b > 0, b  1, and x is any real number. For instance, f(x) = 3 x and g(x) = 0.5 x are exponential parent functions. Definition of Exponential Function

6 The graph of f(x) = b x, b > 1 y x (0, 1) Domain: (– ,  ) Range: (0,  ) Horizontal Asymptote y = 0 Graph of Exponential Function (a > 1) 4 4 Exponential Growth

7 The graph of f(x) = b x, 0 < b < 1 y x (0, 1) Domain: (– ,  ) Range: (0,  ) Horizontal Asymptote y = 0 Graph of Exponential Function (0 < a < 1) 4 4 Exponential Decay

8 Example: Sketch the graph of y = 2 x. x xy(x, y) -2¼(-2, ¼) ½(-1, ½) 01(0, 1) 12(1, 2) 24(2, 4) y 2–2 2 4 Example: Graph f(x) = 2 x

9 Definition of the Exponential Function Here are some examples of exponential functions. f (x) = 2 x g(x) = 10 x h(x) = 3 x Base is 2.Base is 10.Base is 3. Put these in your calculator as y 1 =, y 2 =, y 3 = And graph them simultaneously

10 When base is a fraction Graph the following on your calculator at the same time y 1 = (1/2) x y 2 = (3/4) x y 3 = (7/8) x

11 Example: Sketch the graph of g(x) = 2 -x. State the domain and range. x y The graph of this function is a reflection the graph of f(x) = 2 x in the y- axis. f(x) = 2 x Domain: (– ,  ) Range: (0,  ) 2 –2 4 Example: Reflection of Graph

12 The graph of f(x) = e x y x 2 – xf(x)f(x) Graph of Natural Exponential Function f(x) = e x

13 The irrational number e, where e  … is used in applications involving growth and decay. It is a key on your calculator in the first comlum 2 nd LN The number e

14 What type is it?? You must know if you are graphing a growth or decay equation? Let’s look at some examples

15 Reflection Transformations

16 Reflections Change Type of Exponential

17 Growth or Decay??

18 Growth or Decay??

19 Growth or Decay??

20 Growth or Decay??

21 Growth or Decay??

22 Growth or Decay??

23 Growth or Decay??

24 Homework Worksheet 11-1