Unit 6: Exponential Functions L1 – Graphs of Exponential Functions Let’s compare the following two functions: f(x) = 2x g(x) = 2x x y -3 -2 -1 1 2 3 x y -3 -2 -1 1 2 3

For the graph of f(x) = 2x, as x increases by 1, how do the y-values change? They increase by 2 (added) For the graph of g(x) = 2x, as x increases by 1, how do the y-values change? They are multiplied by 2 Will the graph of g(x) = 2x ever touch the x-axis? Why or why not? No, 2x will never = 0. What is the domain and range of f(x) = 2x? D: (-∞, ∞) R: (-∞, ∞) What is the domain and range of g(x) = 2x? D: (-∞, ∞) R: (0, ∞) f(x) = 2x is an example of a linear function. g(x) = 2x is an example of an exponential function.

Practice 1) Graph f(x) = 3 • 2x over the interval -2 ≤ x ≤ 2. x y -2 -1 1 2 a) What is the y-intercept? 3 b) How are the y-values changing? They are multiplied by 2 c) Is the graph increasing or decreasing? increasing d) What is the range of this function over the interval -2 ≤ x ≤ 2? [.75, 12]

2) Graph f(x) = 8(1/2)x over the interval -2 ≤ x ≤ 2. y -2 -1 1 2 a) What is the y-intercept? 8 b) How are the y-values changing? They are multiplied by 1/2 c) Is the graph increasing or decreasing? decreasing d) What is the range of this function over the interval -2 ≤ x ≤ 2? [2, 32]

Exponential Functions are of the form y = a • bx Notice that the variable x is in the exponent.   “a” is always the y-intercept of the graph. “b” is always the factor that each y-value is multiplied by. If b › 1, then the graph is strictly increasing . If 0 ‹ b ‹ 1, then the function is strictly decreasing .

3) Graph f(x) = 2 • 3x over the interval -1 ≤ x ≤ 3. y -1 1 2 3 a) What is the y-intercept? 2 b) How are the y-values changing? Multiplied by 3 c) Is the graph increasing or decreasing? increasing d) What is the range of this function over the interval -2 ≤ x ≤ 2? [2/3, 54]  

For each of the following a) Determine the y-intercept b) Determine if the function’s graph will be increasing or decreasing. 1) f(x) = 5 • (0.25)x 2) g(x) = 3(4.5)x a) 5 a) 3 b) decreasing b) increasing