Exponential Functions and the mapping rule QUESTION!

AJ22

New member
Joined
Sep 21, 2021
Messages
12
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
Joined
Sep 21, 2021
Messages
12
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
Joined
Nov 12, 2017
Messages
12,598
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?
 
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