The exponential function f(x) = 2x undergoes two transformations to
2 answers:
Answer:
Shifting down.
Vertically compressed
Step-by-step explanation:
Given
Required
Determine the translation from f(x) to g(x)
The first translation from f(x) towards g(x) is:
This is derived by:
Where
Notice that, in the above, b (i.e. 7) was subtracted from f(x), this implies that the function shifted down
The next translation that resulted in g(x) is:
This is derived by:
By comparison:
Since the value of a is less than 1, then f'(x) is vertically compressed to give g(x).
Hence, the transformations that apply from f(x) to g(x) are:
- Shifting down.
- Vertically compressed
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Answer:
A.
Step-by-step explanation:
The options are:
For this exercise it is important to remember that, by definition, the Exponential parent functions have the form shown below:
Where "a" is the base.
There are several transformations for a function f(x), some of those transformations are shown below:
1. If and
, then the function is stretched vertically by a factor of "b".
2. If and
, then the function is compressed vertically by a factor of "b"
Therefore, based on the information given above, you can identify that the function that represents a vertical stretch of an Exponential function, is the one given in the Option A. This is:
Where the factor is:
And