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

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

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

Graph 2 basic shapes C) y = log b x D) y = log 1/b x 5 -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

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

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

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

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

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

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