Exponential Functions and the mapping rule QUESTION!

AJ22

New member
Hey,
I was doing some functions review and learned about how to plot new coordinates for a transformed graph using the mapping rule.
(x,y) (x/b + c, ay + d)

This concept seems to work with most types of functions such as quadratic and sine functions. However, for exponential functions this does not seem to be working.
For 2^x some coordinates include (0,1), (2,4), (4,16)...
When I want to apply a transformation of y = 3^(x+2) - 1, I get a mapping rule of (x-2, y-1).
So now when I take the coordinates of the parent function and sub them into this rule I get (-2,0), (0,3), (2,15)...

Using demos and graphing this, these coordinates are not part of the graph? Does this rule not apply to this function?

AJ22

New member
Nevermind I finally understood where I went wrong....I thought the original function was 2^x but in this case it was 3^x

Dr.Peterson

Elite Member
Hey,
I was doing some functions review and learned about how to plot new coordinates for a transformed graph using the mapping rule.
(x,y) (x/b + c, ay + d)

This concept seems to work with most types of functions such as quadratic and sine functions. However, for exponential functions this does not seem to be working.
For 2^x some coordinates include (0,1), (2,4), (4,16)...
When I want to apply a transformation of y = 3^(x+2) - 1, I get a mapping rule of (x-2, y-1).
So now when I take the coordinates of the parent function and sub them into this rule I get (-2,0), (0,3), (2,15)...

Using demos and graphing this, these coordinates are not part of the graph? Does this rule not apply to this function?
Presumably your rule applies to the transformed function g(x) = af(bx + c) + d. If so, it is correct, and applies to any function f.

In your example, taking f(x) = 3^x, you have g(x) = f(x + 2) - 1, and indeed the point (x, y) transforms to (x - 2, y - 1).

You didn't state what the original points are that you are transforming; I would normally use (-1, 1/3), (0, 1), and ( 1, 3), but perhaps you are using the last two and (2, 9). These four points transform to (-3, -2/3), (-2, 0), (-1, 2), and (0, 8).

Can you show what points you used, and how you transformed them?