When given a graph like this one, what criteria do you usually look for to determine whether it's an exponential or power function?
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When given a graph like this one, what criteria do you usually look for to determine whether it's an exponential or power function?
Hi Allen,
Thank you for your question.
The first thing I would look for is the y-intercept. If the graph crosses through the origin, it would most likely be a power function.
As the general equation for a power function is f(x) = a*(x)^b, when the x value is 0, y value would also be zero. (This means that unless there is a vertical translation, all power function crosses through the origin).
On the other hand, as the general equation for an exponential function is f(x) = a*(b)^x, when the x value is 0, y value would be a, since b^(0) would be 1. Hence, unless there is a vertical translation, all exponential function does not cross through the origin.
For this question, as the graph does not cross through the origin, it is most likely that it would be an exponential function. (Also, as we didn't deal with vertical translations in this unit, I think you can assume the function type from it's y-intercept).
Does this answer your question?