1. Objectives: 1.Be able to graph the exponential growth parent function. 2.Be able to graph all forms of the exponential growth function Critical Vocabulary: Exponential, Asymptote Warm Up: Evaluate each expression for x = 3 and x = -2 (NO DECIMAL ANSWERS) 1. 3 x 2. 63 x 3. 2 x + 5

2. I. Exponential Growth Function Graph: f(x) = 2 x x f(x) 01 2 34-2-3-4 Parent Function: f(x) = b x, where b > 1 Asymptote: A line that a graph gets closer and closer to but never touches Where is the Asymptote? What is the Domain? What is the Range?

3. f(x)= 2 x versus f(x) = -2 x REFLECTIONS!!!! f(x)= 2 x versus f(x) = 32 x The graph increased quicker!!!! f(x)= 2 x versus f(x) = ½2 x f(x)= 2 x versus f(x) = 2 x+1 All points shifted left 1!!!! The graph increased slower!!!! I. Exponential Growth Function

4. f(x)= 2 x versus f(x) = 2 x-1 f(x)= 2 x versus f(x) = 2 x + 1 All points shifted up 1!!!!All points shifted right 1!!!! f(x)= 2 x versus f(x) = 2 x - 1 All points shifted down 1!!!! I. Exponential Growth Function

5. f(x) = ab x-h + k a: Determines size and directions Positive: increases left to right Negative: decreases left to right lal > 1: Changes quicker lal < 1: Changes slower lal = 1: Parent rate of change h: Shifts the graph left or right k: Shifts the graph up or down Example 1: f(x) = -52 x+3 – 2 Reflects Quick change Shifts L3 Shifts D2 Example 2: f(x) = 2 x-4 Asymptote: y = -2 Directions: List the characteristics of each exponential growth function Example 3: f(x) = -½2 x + 4 Example 4: f(x) = -52 x-2 - 7 I. Exponential Growth Function

6. Objectives: 1.Be able to graph the exponential DECAY parent function. 2.Be able to graph all forms of the exponential functions (Growth and Decay) Critical Vocabulary: Exponential, Asymptote Warm Up: List the 5 characteristics of f(x) = -¼ 2 x-5 - 6

7. II. Exponential Decay Function x f(x) 01 2 34-2-3-4 Asymptote: A line that a graph gets closer and closer to but never touches Where is the Asymptote? What is the Domain? What is the Range? Graph: f(x) = ½ x Parent Function: f(x) = b x, where 1 > b > 0

8. f(x)= ½ x versus f(x) = -½ x REFLECTIONS!!!! f(x)= ½ x versus f(x) = 3 ½ x The graph decreased quicker!!!! II. Exponential Decay Function f(x)= ½ x versus f(x) = ½ ½ x f(x)= ½ x versus f(x) = ½ x+1 All points shifted left 1!!!! The graph decreased slower!!!!

9. f(x)= ½ x versus f(x) = ½ x-1 f(x)= ½ x versus f(x) = ½ x + 1 All points shifted up 1!!!! All points shifted right 1!!!! II. Exponential Decay Function f(x)= ½ x versus f(x) = ½ x - 1 All points shifted down 1!!!!

10. f(x) = ab x-h + k a: Determines size and directions Positive: increases left to right Negative: decreases left to right lal > 1: Changes quicker lal < 1: Changes slower lal = 1: Parent rate of change h: Shifts the graph left or right k: Shifts the graph up or down II. Exponential Decay Function

11. III. Graphing an Exponential Growth and Decay Function Example 5: Graph: f(x) = 24 x+2 + 1 No reflection Quick Change Shifts L2 Shifts U1 x f(x) -2 3 9 0 33 -3 3/2 -4 9/8 Domain: All Real Numbers Range: y > 1 Asymptote: y = 1 SPECIAL NOTE: When creating your table, the number in the middle (-2) will be whatever value of x would make the exponent turn into zero. Exponential Growth

12. Example 6: Graph: f(x) = 2½ x-1 + 2 ____________________ x f(x) Domain: ____________ Range: _____________ III. Graphing an Exponential Growth and Decay Function ____________________ Type: _________________

13. Page 482 #3-23 odds (11 problems) Directions: All Graphs require characteristics, domain and range Page 489 #3-21 odds (10 problems)