Question

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)?

Answer 1

C.

Multiplying the x^3 term by 4 means you're stretching it vertically, adding the minus sign means you're flipping it about the x-axis, and subtracting 5 means you're moving it down by 5 units.

Answer 2

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.

Explanation:

Given : The graph
`f(x)=x^3` and
`g(x)=-4x^3-5`

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

Solution :

Let the parent function be
`f(x)=x^3`

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
`f(x) =x^3 \rightarrow \text{Vertically stretch by 4} \rightarrow 4x^3`

Rotation about x -axis:

`(x, y) \rightarrow (x, -y)`

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

i,e
`4x^3 \rightarrow \text{Rotation about x- axis} \rightarrow -4x^3`

Shifting down : f(x)→f(x)-b

Subtracting 5 means you are moving it down by 5 units

`-4x^3 \rightarrow \text{Shifted down by 5 units} \rightarrow -4x^3-5=g(x)`

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.