Mathematics, 17.12.2019 19:31 emwvoidsnake

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)?

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

Answers: 2

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Answer from: nathancar

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 from: mazielynn84

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 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.

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

Answer from: Quest

the formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

from a table we have

$x_1=-4,\ y_1=7\\\\x_2=-2,\ y_2=5$

substitute:

$m=\dfrac{5-7}{-)}=\dfrac{-2}{2}=-1$

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0

answer: the function g(x) has the greatest slope.
The functions, f(x) and g(x) , are shown below. x f(x) -4 7 -2 5 0 3 2 1 4 -1 which function has the

Answer from: Quest

total amount to be paid = $19.5

step-by-step explanation:

given ,

original price = $25.99

discount = 25%

discount amount = 25% of original price

discount amount = 25/100 * 25.99

discount amount = $6.49

hence , the total amount to be paid = original price - discount amount

= $25.99 - $6.49

=$19.5

total amount to be paid = $19.5

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

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