SP#3: Unit I Concept 1- Graphing Exponential Functions

Make sure to pay special attention to the asymptote and the x/y intercepts. The asymptote for exponential functions is from the k in the equation y= a x b^(x-h) + k, so you must remember to set it make it y=K not just k. When solving for the x or y intercepts, be sure to remember that is possible to end up with undefined answer; all that means is that there is no x/y intercept.

1. Find a, b, h, and k. Refer to y= a x b^(x-h) + k. *Remember that for h just put the opposite since it shows as x+1, it is actually -1 since 2 negatives make a positive.

2. Calculate the asymptote. Asymptote of exponential equations is y=k. So the asymptote would be y=  -2, not just -2 in its own. Then, draw the asymptote on the graph.

3. Solve for the x-intercept. Plug in 0 for y and solve. This will review your knowledge on solving exponential equations. Since you can't take the log or natural log of a negative number and zero, the answer will be undefined and no x-intercept. This is also logical because since the graph is below the asymptote of y=-2, then there in no way for it to cross it, let alone intersect the x axis.

4. Solve for y-intercept. Substitute x with 0 and solve. Plot the point on the graph.

5. Write domain in proper notation. Domain of an exponential function will always be (-infinity, infinity), which just means there are no x value restrictions.

6. Write the range in proper notation. This depends on the asymptote and graph. Since the graph is below the asymptote, it would be (-infinity, -2). 

7. Find 4 key points using a graphing calculator. Plot them on the graph.

8. Draw the graph by connecting the points and following the asymptote.