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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)?

PLEASE SOMEONE HELP ME PLATO If the parent function fx 3sqrtnx is transformed to gx 3sqrtnx24 which is the graph of gx class=
PLEASE SOMEONE HELP ME PLATO If the parent function fx 3sqrtnx is transformed to gx 3sqrtnx24 which is the graph of gx class=
PLEASE SOMEONE HELP ME PLATO If the parent function fx 3sqrtnx is transformed to gx 3sqrtnx24 which is the graph of gx class=

Respuesta :

stevengeeky

Answer:

(A)

Step-by-step explanation:

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

Functionally, if we have any function [tex]f(x)[/tex]

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

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

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

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

Answer:

A.

Step-by-step explanation:

Givens:

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

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

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.

Ver imagen jajumonac

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