Question

How does the graph of g(x) = (x + 4)3 − 6 compare to the parent function f(x) = x3?

Answer 1

The parent function is
`f(x)=x^(3)`

The transformed function is
`g(x)=(x+4)^(3) -6`

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
`f(x)` and
`g(x)`.

Now, you can get this answer by using the rules to translate functions:

• If you add units to the x-variable, the graph will move to the left, if you subtract units to that variable, the graph will move to the right.
• If you add units to y-variable, the graph will move upwards. If you subtract units from that variable, the graph will move downwards.

Answer 2

g(x) is shifted 6 units to the left

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