This is the new update of the question

d

Step-by-step explanation:

If x represents the slant height, the graph would be a straight line.

If x represents the radius, the graph would be a parabola.

Looking at the answers, we're looking for x to be the slant height, so we're looking for a straight line.

We are looking for g(x). Answers a and b are wrong.

In g(x) r is fixed to 5 (this is given). So the slant height in the smallest possible cone would still be at least 5.

So the domain is x > 5.

d is your answer.

We have this formula for the surface area of a cone

SA = pi*r*s + pi*r^2

The pi*r^2 portion is the flat bottom part of the cone, which is a circle of radius r. The pi*r*s portion is the lateral surface area. This is the triangular part of the cone, so to speak.

"one of the functions represents the surface area of a cone with radius 5 and slant height x". So we can say r = 5 and s = x to go from this

SA = pi*r*s + pi*r^2

to this

SA = pi*5*x + pi*5^2

SA = 5pi*x + 25pi

y = 5pi*x + 25pi

note how this is a linear function in the form y = mx+b

"The other function represents the surface area of a cone with slant height 5 and radius x", meaning s = 5 and r = x

SA = pi*r*s + pi*r^2

SA = pi*x*5 + pi*x^2

SA = 5pi*x + pi*x^2

SA = pi*x^2 + 5pi*x

y = pi*x^2 + 5pi*x

This is a quadratic function due to the x^2 term. This graphs out a parabola.

The graph given to us has f(x) as the parabola (it's the bowl shaped graph) while g(x) is the straight line

Therefore,

f(x) = pi*x^2 + 5pi*x

g(x) = 5pi*x + 25pi

f(x) is the cone with radius x and slant height 5

g(x) is the cone with radius 5 and slant height x

Keep in mind that the slant height of a cone forms the hypotenuse of a right triangle when you do a vertical cross section. If the radius is 5, then the leg of the triangle is 5. The hypotenuse is always longer than either leg, so the hypotenuse x must be larger than 5. A right triangle would not be possible with the hypotenuse x < 5 (you would have to shrink the radius).

50- 250 is correct i did that one too

step-by-step explanation: