I was wondering is there a way to always be able to graph an exponential function and finding the exponential equation from the graph?
I am really struggling with exponential graphs in terms of drawing them gievn the equation and being unable to find the equation given the graph. The tranformations that can be possible are also being quite an obstacle for me. Please help
Perhaps a set of rough rules will help!!
Consider the general form of an exponential function:
(Note that it doesn't have to be the with an 'e', any number works fine, though if you have a negative number there you'll need to adjust this a little the base won't be - this requires complex analysis)- Higher values of A stretches the curve in the vertical direction. Really, the noticeable impact is that A is the y-intercept, but only if there is no constant C added to the exponent
- Higher values of B means the exponent will increase at a faster rate, the right hand side of the exponential will increase its slope noticeably
- C causes a horizontal shift to the left (for positive values) or right (for negative values)
- D causes a vertical shift upwards (positive values) or downwards (negative values)
These rules might seem very wish-washy, and that's because they are, they should only be a rough guide. You aim should be to gradually develop an intuition for what the different parts of the exponential do. Have a play with sketching different functions on
Desmos or something similar, and try to notice the patterns in what you see, that is the best way to develop that intuition