Question

PLEASE SOMEONE HELP ME

PLATO:

If the parent function f(x) = [3]\sqrt[n]{x} is transformed to g(x) =[3]\sqrt[n]{x+2-4] , which is the graph of g(x)?

Answer 1

(A)

Explanation:

The graph of any function (of
`x`) can be shifted horizontally by a number
`h` by replacing every
`x` in the function with
`x - h`. And, if we want to shift the graph vertically, we simply add the number we want to shift by (which I'll call
`k`) to every output of the function.

Functionally, if we have any function
`f(x)`

We can shift it horizontally by
`h` units and vertically by
`k` units by creating a function
`g(x) = f(x - h) + k`.

Notice that in this case,
`g(x) = f(x - (-2)) - 4`. So the graph of
`f(x)` is shifted 2 units to the left, and 4 units down.

Or if this is too abstract of an explanation, then notice

`\sqrt[3]{x + 2}  - 4` looks similar to
`\sqrt[3]{x - h}  - k`. Specifically, if h = -2 and k = -4 (the graph is shifted two units left and 4 units down), then the function becomes equivalent to
`g(x)`

Answer 2

A.

Explanation:

Givens:

The parent function:
`f(x)=\sqrt[3]{x}`

The transformed function:
`g(x)=\sqrt[3]{x+2}-4`

You can observe that the transformation was

1. 2 units added to x-variable.
2. 4 units subtracted to y-variable.

Now, remember, where we add to x-variable, we'll move the function to the left. When we subtract units from y-variable, we'll move the function downwards.

So, basically, we have to look for the function which is moved to the left 2 units and downside 4 units.

Having said that, you can deduct that the right answer is graph A.

However, in the image attached you can observe a comparison between the parent function and the transformed function. Notice that the transformed one is the same as graph A.