4.3 Exponential Functions

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Presentation transcript:

4.3 Exponential Functions What is the longest running game show?

Laws of Exponents - Review

Exponential Functions An exponential function is a function of the form: where a is a positive real number (b > 0) and b ≠ 1. x y x y f (x) = 2x f (x) = 5x f (x) = 2x f (x) = (1/2)x f (x) = (1/5)x f (x) = (1/2)x

Properties of Exponential Functions Domain/Range Intercepts Asymptotes Inc or Dec Common Points Other Domain: (-∞,∞) Range: (0,∞) x-int: None y-int: (0,1) y = 0 as x -∞ y = 0 as x ∞ Increasing and 1-to-1 Decreasing and 1-to-1 Graph is smooth/continuous (no corners/gaps)

Exponential Transformations Determine the equation for each graph using transformations of the function y = 5x. 1) 2) y = 5x 3) 4)

Exponential Transformations Determine the equation for each graph using transformations of the function y = 5x. 5) 6) 7) 8)

Exponential Equations

Exponential Equations

Exponential Equations

Group Challenge! (1/2 Sheet)

4.3 Exponential Functions Homework #14: p.284 #29-36, 53-65 odd, 71-74, 75, 77