For the function f(x) = -2x^2, if the domain is (-3, 0, 3), find the range. A. (0, -36)
B. (0, -18)
C. (-18, 0, 18)
D. (-36, 0, 36)

option c

Step-by-step explanation:

 Choice B

Range = {0, -18}

Explanation:

The domain is the set of allowed x inputs.

In this case, we're only allowed to plug in x = -3, x = 0 or x = 3.

Plug x = -3 into the function to get

f(x) = -2x^2

f(-3) = -2(-3)^2

f(-3) = -2*9

f(-3) = -18

The input x = -3 leads to the output y = -18

So -18 is one value in the range.

Repeat for x = 0

f(x) = -2x^2

f(0) = -2(0)^2

f(0) = -2*0

f(0) = 0

That means y = 0 is also in the range

Repeat for x = 3

f(x) = -2x^2

f(3) = -2(3)^2

f(3) = -2*9

f(3) = -18

We get -18 again like we did earlier. This is because (-3)^2 and (3)^2 have the same result.

The outputs we got were: -18, 0, -18

Effectively, the range is {-18, 0} which is the same as {0, -18} so that's why choice B is the answer.

Note: We don't list any repeat values when it comes to the domain or range.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4