How do you determine a equation from a expoential function graph ? Please explain by using a basic graph with a expoential function?

Asked on by nhl123

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You should start with the graph of exponential function y=e^x.

If you need to find the equation that results if you reflect the graph about the line y=1, start by reflecting the graph about y=0.

The movement of the line y=1 to y=0 makes the graph y=e^x to go 1 unit down.

This movement may be written such that y=e^x - 1.

You should come up with the substitution y=-y to produce the reflection about x axis (y=0).

-y = e^x - 1 => y = 1 - e^x

Moving back the graph yields y = 1 - e^x + 1 => y = 2 + e^x

The graph of the function y = 2+e^x is black and the reflection line y = 1 is green.


The equation that results from reflection of the exponential graph around the line y=1 is y = 2 + e^x.  

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