1. 4.3 Exponential Functions
What is the longest running game show?

2. Laws of Exponents - Review

3. 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

4. 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)

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

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

7. Exponential Equations

8. Exponential Equations

9. Exponential Equations

10. Group Challenge! (1/2 Sheet)

11. 4.3 Exponential Functions
Homework #14: p.284
#29-36, odd, 71-74, 75, 77