Answer: [tex]B.\ g(x)=\frac{1}{4}(x+3)^3[/tex]
Step-by-step explanation:
Some transformations for a function f(x) are shown below:
1. If [tex]f(x-k)[/tex], the function is shifted right "k" units.
2. If [tex]f(+k)[/tex], the function is shifted left "k" units.
3. If [tex]bf(x)[/tex] and [tex]b>1[/tex], the function is stretched vertically by a factor of "b".
4. If [tex]bf(x)[/tex] and [tex]0<b<1[/tex], the function is compressed vertically by a factor of "b".
In this case, you know that the parent function f(x) is:
[tex]f(x)=x^3[/tex]
If the graph of the function g(x) is obtained by compressing vertically and shifting the function f(x) to the left, then:
[tex]g(x)=bf(x+k)[/tex] and [tex]0<b<1[/tex]
Based on this, you can identify that the following function could be the equation of the g(x):
[tex]g(x)=\frac{1}{4}(x+3)^3[/tex]
