Captain Jabbamathee's steps to graph the natural logarithm function y = |log x| are: 1. Graph the inverse function y = 5^x to determine the asymptote and domain and range. 2. Graph y = log x by reversing the x and y values of the inverse graph y = 5^x. 3. Make all values positive to account for the absolute value. The graph has an asymptote of x = 0, domain of (0, ∞), range of [0, ∞), and increases and decreases.

1. Captain Jabbamathee’s steps to success: Logs and Exponents 7.2 The Natural Logarithm Function by flickr user mseery

2. Graphing Graph the function: y = |log x| Need to find: a) asymptote b) domain c) range d) is it increasing or decreasing Using three main steps.. 5

3. Step 1 Graph y = 5^x which is the inverse of y = log x To choose a value for x, you would look to the x-axis. Ex. When x = 1: 5^1 = 5, so the y-coordinate = 5 Ex. When x = -1: 5^(-1) = ½, so y-coordinate = 1/2 5

4. Step 2 Graphing y = log x is the same as graphing the inverse of y = 5^x Therefore the values for x and y would be reversed This means if the original graph had points (1,5) than the inversed points would be (5,1). All the inverse points would make a new graph, which is a reflection of the original graph that was reflected over the line y = x. 5

5. Step 3 This graph is an absolute value, therefore all the values have to be positive. The graph bounces off the x-intercept and back into the positive quadrants.

6. Solutions The asymptote is x = 0 The domain is (0, ∞) The range is [o, ∞) The graph is both increasing and decreasing