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Thursday, October 24, 2013

SP#3: Unit I Concept 1 - Graphing Exponential Functions & Identifying All Needed Parts

In this problem, you need to make sure to check if there's an x-intercept or not. You can tell by checking if there's a negative log, if there is, then there is no x-intercept. Also, make sure to write your domain and range correctly. On an exponential graph, domain is always negative infinity to infinity.

The first step you would have to do is label your variables (a=-3, b=2, h=1, k=-2). Next, you find your y-intercept, this is basically just y=k (y=-2). Then, you find your x-intercept, and from the picture below, you can see that there can never be a negative natural log. As a result, there is no x-intercepts. The next step is to find your y-intercept. From the step-by-step work that I've shown below, the y-intercept is (0, -7/2) or it can also be written as (0, -3.5). The domain would always be negative infinity to positive infinity since it's an exponential graph. Lastly, the range would be negative infinity to negative two. It's negative infinity because the graph is below the asymptote and the negative two came from the asymptote.

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