Which of the following best describes the graph below?

a. it us a one-to-one function

b. it us a function but it is not one-to-one

c. it is not a function.

d. it is a many-to-one function.

Option: A is the correct answer.

             A. it is a one-to-one function  

Function--

A graph is one-one when a vertical line is drawn parallel to the y-axis and passing through the domain should intersect the curve exactly once.

i.e. it passes a vertical line test.

One-one function-

A function is said to be one-one if corresponding to each x we get a distinct y-value.

i.e. No two x have the same y-value.

Also it can be seen from the graph when any horizontal line is drawn parallel to the x-axis then the line intersect the curve atmost once.

        i.e. it passes the horizontal line test.

Many-to-one function--

A function is many to one when many x-values are mapped to same y-value.

Clearly from the graph we see that the graph is a one-to-one function.

           ( As it passes the horizontal line test)

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.

answer: the answer is ann