Question

PLEASE SOMEONE HELP ME

Answer 1

Answer:

A.

Step-by-step 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.

Answer 2

Answer:

(A)

Step-by-step 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 $g(x)$