Answer:
Shifting down.
Vertically compressed
Step-by-step explanation:
Given
[tex]f(x) = 2^x[/tex]
[tex]g(x) = \frac{1}{3}(2^x - 7)[/tex]
Required
Determine the translation from f(x) to g(x)
The first translation from f(x) towards g(x) is:
[tex]f(x) = 2^x[/tex]
[tex]f'(x) = 2^x - 7[/tex]
This is derived by:
[tex]f'(x) = f(x) - b[/tex]
Where
[tex]b = 7[/tex]
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:
[tex]g(x) = \frac{1}{3}(2^x - 7)[/tex]
This is derived by:
[tex]g(x) = a.f'(x)[/tex]
By comparison:
[tex]a = \frac{1}{3}[/tex]
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:
