1. Sec 11-1 Graphs of Exponential and Logarithmic Functions

2. What is an exponential function?
F(x) = ax where a is positive and does not equal 1.
Graph in your calculator a = 2, 3, and 4. What happens as a gets larger?
F(x) = 4x is the steepest!
What is the domain?
What is the range?

3. What if 0 < a < 1?
Graph in your calculator f(x) = ax for a = ½, a = 1/3, a = ¼ and describe what happens.
(1/4)x is the steepest.
What is the domain?
What is the range?

4. What is the inverse of y = ax ?
X = ay
How do we graph it?
Ex: x = 2y

5. How do we solve x = ay for y?
Y = loga(x) means x = ay
Example: y = log2(8)
Means: y is the power of 2 that yields 8.
What’s y?
i.e. 2y = 8.
Y = 3
LOG a (x) = Y
Exponent
Answer
Base

6. Log examples to try… Y = log4 (1/16) Y = log10 (-10) 2 = logb (16)
Impossible
2 = logb (16)
B2 = 16
B = 4 only (base must be positive)
“y is the power of 4 that yields 1/16”
“y is the power of 10 that yields -10”
“2 is the power of b that yields 16”

7. More Log Examples Log(1/2)c = -3 Logx (9) = (2/3) Loga (1) = x Ax = 127
Loga (1) = x
Ax = 1
X = 0 (remember, exponential so x can’t be 1)
“-3 is the power of ½ that yields c”
“2/3 is the power of x that yields 9”
“x is the power of a that yields 1”

8. Write the equations in log form
3y = 12
y = log3 (12)
A5 = 100
5 = loga (100)
4log4(16) = x
Log4x = log416
What is aloga(x)? X
And loga(ax) = x
“y is the power of 3 that yields 12”

9. HW: , #7-25(odd), 29,31,33,39,41,45