SOLUTION: List the transformations, in order, for the following function: f(x)=4-3^x-1 The first thing I did was rewrite the function: f(x)=-3^(x-1)+4

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Question 374505: List the transformations, in order, for the following function:
f(x)=4-3^x-1
The first thing I did was rewrite the function: f(x)=-3^(x-1)+4
- Horizontally shifts 1 unit to the right (because of (x-1))
- Reflects about the x-axis (because of the negative in front of the 3)
- Vertically shifts 4 units up (because of the +4)
Is this correct?
Does the function vertically stretch by a factor of 3?
In my notes a compress/stretch is said to be: a > 1 then vertically stretches by factor of a
0 < a < 1 vertically compresses by factor of a
But the instructor walked us through this problem but did not mention anything about a vertical stretch or compression.
Answer by jsmallt9(3759) (Show Source):
You can put this solution on YOUR website!
The first thing I did was rewrite the function: f(x)=-3^(x-1)+4
- Horizontally shifts 1 unit to the right (because of (x-1))
- Reflects about the x-axis (because of the negative in front of the 3)
- Vertically shifts 4 units up (because of the +4)
Is this correct?

Yes.

Does the function vertically stretch by a factor of 3?

No.

In my notes a compress/stretch is said to be: a > 1 then vertically stretches by factor of a
0 < a < 1 vertically compresses by factor of a

This is all correct. However, your "base" function, from which the transformations are made, is

The "3" is part of the base function. If you had

Then the "2" would be the vertical stretch factor. Your f(x) does not have any vertical stretch factor (other than 1 (which is "no stretch")).

SOLUTION: List the transformations, in order, for the following function: f(x)=4-3^x-1 The first thing I did was rewrite the function: f(x)=-3^(x-1)+4 - Horizontally shifts 1 unit to