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Objectives: Be able to graph the exponential growth parent function.

Exponential Growth Functions. Objectives: Be able to graph the exponential growth parent function. 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)

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Objectives: Be able to graph the exponential growth parent function.

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  1. Exponential Growth Functions • Objectives: • Be able to graph the exponential growth parent function. • 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. 3x 2. 6•3x 3. 2x + 5

  2. I. Exponential Growth Function Parent Function: f(x) = bx, where b > 1 Graph: f(x) = 2x 2 -4 -3 -2 -1 0 1 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?

  3. I. Exponential Growth Function f(x)= 2x versus f(x) = -2x f(x)= 2x versus f(x) = 3•2x The graph increased quicker!!!! REFLECTIONS!!!! f(x)= 2x versus f(x) = ½•2x f(x)= 2x versus f(x) = 2x+1 All points shifted left 1!!!! The graph increased slower!!!!

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

  5. I. Exponential Growth Function f(x) = abx-h + k a: Determines size and directions h: Shifts the graph left or right Positive: increases left to right k: Shifts the graph up or down Negative: decreases left to right lal > 1: Changes quicker lal < 1: Changes slower lal = 1: Parent rate of change Directions: List the characteristics of each exponential growth function Example 1: f(x) = -5•2x+3 – 2 Example 2: f(x) = 2x-4 • Reflects Example 3: f(x) = -½•2x + 4 • Quick change Example 4: f(x) = -5•2x-2 - 7 • Shifts L3 • Shifts D2 • Asymptote: y = -2

  6. Exponential Decay Functions • Objectives: • Be able to graph the exponential DECAY parent function. • 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•2x-5 - 6

  7. II. Exponential Decay Function Parent Function: f(x) = bx, where 1 > b > 0 Graph: f(x) = ½x 2 -4 -3 -2 -1 0 1 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?

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

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

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

  11. III. Graphing an Exponential Growth and Decay Function Example 5: Graph: f(x) = 2•4x+2 + 1 Exponential Growth -2 -1 -4 -3 0 • No reflection 9/8 3/2 3 9 33 • Quick Change • Shifts L2 • Shifts U1 • Asymptote: y = 1 Domain: All Real Numbers Range: 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.

  12. III. Graphing an Exponential Growth and Decay Function Example 6: Graph: f(x) = 2•½ x-1 + 2 Type: _________________ • ____________________ • ____________________ • ____________________ • ____________________ • ____________________ Domain: ____________ Range: _____________

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

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