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

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absor201 absor201 · Answer 1 · 2019-05-21T18:17:57+02:00

Answer:

Option A is correct.

Step-by-step explanation:

f(x)=x^3

and g(x) = (x-3)^3 +4

In general, if f(x) = (x-h) then the graph is shifted to the right h units

and if f(x) = f(x) + h then the graph is shifted up h units.

In the given question f(x) = x^3 and g(x) = (x-3)^3 +4

The graph g(x) is shifted 3 units to the right ((x-3)^3) and 4 units up ((x-3)^3 +4).

So, Option A is correct.

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MrRoyal MrRoyal · Answer 2 · 2021-10-28T11:54:45+02:00

Transformation involves changing the position of a function.

The transformation from f(x) to g(x) is: (a) shifting 3 units left and 4 units up.

The parent function is given as:

[tex]\mathbf{f(x) = x^3}[/tex]

When a function is translated to the right by h units, the rule of transformation is:

[tex]\mathbf{(x,y) \to (x - h,y)}[/tex]

So, we have:

[tex]\mathbf{f'(x) = (x - 3)^3}[/tex]

Next, the function is translated up by 4 units.

The rule of transformation is:

[tex]\mathbf{(x,y) \to (x,y+4)}[/tex]

So, we have:

[tex]\mathbf{g(x) = (x-3)^3 + 4}[/tex]

Hence, g(x) compares to f(x) by (a) shifting 3 units left and 4 units up.