Answer:
g(x) is shifted 6 units to the left
Step-by-step explanation:
Lets try to simplify g(x) since has a few extra terms:
g(x)= 3x+12-6=3x+6
Now it is easier to compare the two functions.
We can tell that they both have the same slope, both differs on a extra term
This term tell us that the g(x) is shifted to the left (it is positive 6)
Another approach to the solution is to plot the two functions together by obtaining the crossing points with the 'y' axis and with the 'x' axis
the result is shown in the attached picture
Answer:
The parent function is [tex]f(x)=x^{3}[/tex]
The transformed function is [tex]g(x)=(x+4)^{3} -6[/tex]
In the transformed function, you can observe that there's being added four units to x-variable, and there's being subtracted six units from x-variable.
These transformation means that the parent function is being moved 4 units leftwards and 6 units downwards, that's basically the relation between [tex]f(x)[/tex] and [tex]g(x)[/tex].
Now, you can get this answer by using the rules to translate functions:
