# Transformations of exponential functions

## Homework Statement

Im not sure what each of the variables do in

y=cax-p +q

## The Attempt at a Solution

my understanding is that
-q is for vertical shifts/transformations
-p is for horizontal shifts/transformations
-and c is for vertical stretching
not sure what a is for

thanks!

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vela
Staff Emeritus
Homework Helper
Try plotting two exponential functions with different a's, e.g., y=2x and y=3x, to see the effect of changing a.

well according to that, a is for vertical stretching but, if that is the case, then what is c for?

vela
Staff Emeritus
Homework Helper
Sorry, those particular values weren't the best choices. Try looking at y=1x and y=(1/2)x as well. You'll see it's not a simple matter of vertical scaling.

Ray Vickson
Homework Helper
Dearly Missed
well according to that, a is for vertical stretching but, if that is the case, then what is c for?
Nope: 'a' is for horizontal stretching (that is,for changing the "shape", from nearly straight to highly curved). To see this, you need to make sure the vertical scale is the same in both plots, so that the value of y at x = 0 is the same in both.

RGV

Mark44
Mentor
In your function, y = cax - p + q, the only parameters you need to be concerned with (IMO) are c, p, and q. All of the transformations you describe can be thought of as relative to the graph of y = ax.

If you actually do need to say something about a, you need to have some other exponential function to compare y = ax with.

Nope: 'a' is for horizontal stretching (that is,for changing the "shape", from nearly straight to highly curved). To see this, you need to make sure the vertical scale is the same in both plots, so that the value of y at x = 0 is the same in both.

RGV
ohhh... its for horizontal stretching...thanks!