How does the graph of g(x) = −(x + 3)^4 compare to the parent function of f(x) = x^4?
a. g(x) is shifted 3 units to the right and 1 unit up.
b. g(x) is shifted 3 units to the right and 1 unit down.
c. g(x) is shifted 3 units to the right and reflected over the x-axis.
d. g(x) is shifted 3 units to the left and reflected over the x-axis.

Option D

g(x) is shifted 3 units to the left and reflected over the x-axis.

Step-by-step explanation:

If we have a function f(x) and make a transformation of the form:

Then it is true that:

If the graph of g(x) is equal to the graph of f(x) displaced h units to the left

If the graph of g(x) is equal to the graph of f(x) displaced h units to the right

Also if we have a function f(x) and perform a transformation of the form:

Then it is true that:

The graph of g(x) is equal to the graph of f(x) reflected on the x axis.

In this case and

So

Then . Therefore the graph of g(x) is equal to the graph of f(x) displaced 3 units to the left and reflected on the x axis

The answer is the option D

2? if not the correct answer you might need to provide more information

step-by-step explanation:

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.