1. Graphing Logarithmic Functions
OBJ:  To write an equation for
the inverse of an
exponential function or a
logarithmic function
 To draw the graph of a
 To read and interpret the
graph of a logarithmic
function

2. P394 EX: 1  Graph y = log 3 x 1. Increasing 2. Key Point (1,0)
x y = 3x -2
1/9 -1
1/3 1 3 2 9 y x 5 -5
3y y
1/9 -2
1/3 -1 1 3 9 2
1. Increasing
2. Key Point (1,0)
D: (0, ∞)
R: 
x = 0

3. P395 EX: 2 Graph y=log4x; y=log¼x
4y y -2
1/16 -1
1/4 1 4 2 16
1. Inc and Dec
2. Key Point (1,0)
D: (0, ∞)
R: 
x = 0 y x 5 -5
4-y y -2 16 -1 4 1
1/4 2
1/16

4. Graph 2 basic shapes C) y = log b x D) y = log 1/b x5 -5 y x 5 -5
Note: The graph of Ex 2 can be obtained by reflecting the graph of Ex 1 in the x-axis

5. Graph y = log 2 (x – 3) 1. Inc, C 2. 3 R; (4, 0) 3. D: (3, ∞) 4. R: 5 -5

6. Graph y = log ½ (x + 3) 1. Dec; D 2. 3 L; (-2, 0) 3. D: (-3, ∞)5 -5

7. Graph y = log ½ x + 3 1. Dec, D 2. 3↑; (1, 3) 3. D: (0, ∞) 4. R: 
2. 3↑; (1, 3)
3. D: (0, ∞)
4. R: 
5. x = 0 y x 5 -5

8. Graph y = log 2 (x + 3) – 2 1. Inc, C 2. 3 L, 2↓; (-2, -2)
3. D: (-3, ∞)
4. R: 
5. x = -3 y x 5 -5

9. Graph y = log e (x + 1) – 3 1. Inc, C 2. 1 L, 3↓; (0, -3)
3. D: (-1, ∞)
4. R: 
5. x = -1 y x 5 -5

10. P 394  If y = 2 x what is y – 1 (y inverse)?
x = 2 y
log2x = log 22 y
log2x = y
y = log2x
DEF:  Inverse of an exponential function
y = logbx
NOTE: Since y = 3 x and y = log 3 x are
inverse functions, they are
symmetric with respect to y = x
and the graph of y = 3 x could be
reflected in y = x to obtain
y = log 3 x