UNIT 5: Graphing Exponential Functions

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Presentation transcript:

UNIT 5: Graphing Exponential Functions a = original amount (y-intercept) b = growth factor (1 ± r) r = rate (percent) y = final amount x = unit of measure (time, bounces, etc.) Exponential Growth Exponential Decay End Behavior: End Behavior: Math 3 Hon: Unit 5

Things to know about b cannot be negative b > 1: 0 < b < 1: DOMAIN of all exponential functions is: all real numbers (no restrictions for x) RANGE of exponential functions: Positive “a” Negative “a” Y – INTERCEPT = a y-values follow multiply or divide patterns

Identifying Growth & Decay: What is the factor v. rate? b) c) d) e) f)

Graphing Exponentials (Unshifted) by Hand: Find y-intercept, domain, range, and SKETCH 1. 2. 4. 3.

Write Unshifted Exponential Equation by Hand: Given two points of the exponential graph 1. (0, 3) and (1, 5) 2. (0, -2) and (-1, -8) 3. (0, 7) and (2, 63) 4. (0, 56) and (3, 7)

Graphing Shifted Exponential Functions by Hand: Original : Shifted: x y -2 or -1 a 1 ab 2 ab2 “h”: “k”: Shifted DOMAIN: Shifted RANGE:

Graphing Shifted Exponential Functions by Hand: 1. Describe the Shift: (Up, Down, Left, Right) 2. Describe the Shift: (Up, Down, Left, Right) Original Function and Key Points: Shifted Points: Original Function and Key Points: Shifted Points: 3. Describe the Shift: (Up, Down, Left, Right) 4.Describe the Shift: (Up, Down, Left, Right)

Solving for the vertical shift value (k) of an exponential: Substitute and solve Given: y = 4(2)x + k Given: y = 16(1/2)x + k Given: y = 3x + k (-1, 5) (2, 2) (0, 4) Given: Given: (2, 6) (-1, -1)