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