Transformations of exponential functions

[supernova1203]

Homework Statement

Im not sure what each of the variables do in

y=ca^x-p +q

Homework Equations

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

please help?

thanks!

 

[vela]

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

 

[supernova1203]

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

 

[vela]

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

 

[Ray Vickson]

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]

In your function, y = ca^{x - 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 = a^x.

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

 

[supernova1203]

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!