Which of the following graphs corresponds to the function above

Question

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calculista calculista · Answer 1 · 2019-04-24T23:54:46+02:00

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]f(x)=\sqrt[3]{x-2}[/tex]

we know that

The parent function of f(x) is equal to g(x)

[tex]g(x)=\sqrt[3]{x}[/tex]

The rule of the transformation of g(x) to f(x) is equal to

(x,y)------> (x+2,y)

That means------> The translation is 2 units to the right

Using a graphing tool

The graph in the attached figure

Answer Link

virtuematane virtuematane · Answer 2 · 2019-05-30T06:35:54+02:00

We are given a function f(x) as:

[tex]f(x)=\sqrt[3]{x-2}[/tex]

We know that the function intersects the x-axis when x=2

Since when x=2 we have:

[tex]f(x)=\sqrt[3]{2-2}=\sqrt[3]{0}=0[/tex]

Hence, the graph of the function passes through the point (2,0).

Also, when x<2 then x-2<0

and hence the function will take negative value.

i.e. f(x)<0 when x<2

and when x>2 the f(x)>0

Hence, the graph of the function is attached to the answer.