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The exponential function - if it has a positive exponent - will grow quickly towards positive values of "x". Actually, for small coefficients, it may also grow slowly at first, but it will grow all the time. At first sight, such a function can easily be confused with other growing (and quickly-growing) functions, such as a power function.

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Q: How can you identify exponential function from its graph?
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Related questions

How does the graph of an exponential function differ from the graph of a linear function and how is the rate of change different?

The graph of a linear function is a line with a constant slope. The graph of an exponential function is a curve with a non-constant slope. The slope of a given curve at a specified point is the derivative evaluated at that point.


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Yuo cannot include a graphical illustration here. Take a look at the Wikipedia, under "exponential function" and "logistic function". Basically, the exponential function increases faster and faster over time. The logistics function initially increases similarly to an exponential function, but then eventually flattens out, tending toward a horizontal asymptote.


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an exponential function flipped over the line y=x


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It is an exponential function.


What happens to the graph of an exponential function if b is a function between 0 and 1?

This question appears to relate to some problem for which we have no information. The graph of an exponential function shows a doubling at regular intervals. But we are not told what the role is of b, so we cannot comment further.


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