1. 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

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.

4. 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]

5. 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]

6. 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 .

7. 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]

8. 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) a) 3
b) decreasing b) increasing