Algebra 2 9.2C Graphing Logarithmic Functions
Obj: able to graph logarithmic functions
Complete the tables.
Original/Exponential Inverse/Log Inverse in logarithm form
y = 2
x
x y
-1
0
2
3
Asymptote Asymptote
Recall: The function
y = 2
x
can be shifted around the graph by y = 2
x - h
+ k.
Identify the shift from its original.
1. y = 2
x -4
+ 2 2. y = 2
x+3
- 5
3. Write the inverse for
x
y3=
4. Now write the logarithm form for the inverse in problem 3.
Identify the following, where the graph of
(
)
khxy
b
+−= log shifts the same as you would expect from above.
5.
xy
3
log1+−=
6.
(
)
2log
3
−= xy
Parent__________ Shift_______________ Parent__________ Shift_______________
Exponential form___________ Exponential form___________
Inverse_____________ Inverse_____________
x = 2
y
x y
-1
0
2
3
Definition of Logarithm to Base b
Let b > 0 and x > 0 with b≠1. The logarithm of x with base b is denoted by
yx
b
=log
and is defined as follows.
yx
b
=log
if and only if
y
bx = The expression
x
b
log
is read as the “log base b of x”
Inverse Functions
The inverse of a relation is a set of ordered pairs obtained by switching the coordinates of each ordered pair in the relation.
To find the inverse of a relation that is given by an equation in x and y, switch the roles of x and y in the equation.
