Suppose that f(x)=x^3 and g(x)=-4x^3-5 . which statement best compares the graph of g(x) with the graph of f(x)?

Option C

The graph of g(x) is the graph of f(x) stretched vertically, flipped over the x-axis and shifted 5 unit down.

Step-by-step explanation:

Given : The graph   and

To find : Which statement best compares the graph of g(x) with the graph of f(x)?

Solution :

Let the parent function be

Vertically Stretch:

If y =f(x) , then y = a f(x) gives a vertical stretch if a> 1.

Multiplying the parent function by 4 means you are stretching it vertically,

i,e

Rotation about x -axis:

The minus sign means you are rotating it about the x-axis

i,e  

Shifting down : f(x)→f(x)-b

Subtracting 5 means you are moving it down by 5 units  

Refer the attached figure below.  

Therefore, Option C is correct.

The graph of g(x) is the graph of f(x) stretched vertically, flipped over the x-axis and shifted 5 unit down.

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step-by-step explanation: