1. Table of Contents Logarithmic Function - Graphing Example Sketch the graph of the logarithmic function... First, write the function in its exponential form. Find a few ordered pairs (plug in y, find x)... (1/9, - 2) (1/3, - 1) ( 1, 0) ( 3, 1) ( 9, 2) and plot them on a graph.

2. Table of Contents Slide 2 Logarithmic Function - Graphing Now join the points with a smooth curve... Note that the growth is rapid at first... and then the rate of growth slows. Note also that the graph goes through the point (1,0).   

3. Table of Contents Logarithmic Function - Graphing Slide 3 There is a relationship between the graphs of exponential and logarithmic functions. ExponentialLogarithmic (0,1)(1,0) (1,4)(4,1) (2,16)(16,2) Note that in the corresponding ordered pairs, the order of x and y is reversed, which suggests inverse functions. In fact, exponential and logarithmic functions to the same base are inverse functions.

4. Table of Contents Slide 4 Logarithmic Function - Graphing ExponentialLogarithmic To see the inverse relationship graphically, graph each...

5. Table of Contents Slide 5 Logarithmic Function - Graphing... and then graph both functions on the same coordinate system. Note the symmetry about the line y = x...

6. Table of Contents Slide 6 Logarithmic Function - Graphing Note the following characteristics of the exponential and the logarithmic functions, which are inverse functions. Exp Log Domain: (- ,  )(0,  ) Range: (0,  ) (- ,  ) Intercept: (0,1)(1,0) Asymptote: y = 0 Horizontal x = 0 Vertical  

7. Table of Contents Logarithmic Function - Graphing