The graph of the piecewise function f(x) is shown.

what is the domain of f(x)?
{x | 1 < x < 5}

{x | 1 < x < 5}

{y | −4 < y < 1}

{y | −4 < y < 1}

First of all, it asks for domain, which is allowed x values.

So immediately we can rule out last 2 answer choices.

If you look at the graph, the allowed x values are from 1 to 5.

Note: closed circle means that number is included and open circle means that number is NOT included

Now we see that 1 has closed circle so 1 is included and there is an open circle at 5, so 5 is NOT included.

Correct domain is {x | .

ANSWER: Domain is {x |

i can't see the picture : /

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.