Question

Which of the following could be an example of a function with a range (-∞,a] and a domain [b, ∞) where a < 0 and b < 0?
A. ƒ(x)= √(x-a)+b
B. ƒ(x)=3√(x-b)+a
C. ƒ(x)=-3√(x+a)-b
D. ƒ(x)=-√(x+b)-a

Answer 1

Where do the radicals end? I'm guessing right after the parenthesis?

Answer 2

yes

Answer 3

Well, let's look at the range first. That square root part is always non negative, right?

Answer 4

So looking at each possibility:
A. ƒ(x)= √(x-a)+b
To find the lowest that could be, set the whole radical to 0. So b is the lowest. And as we increase that radical, the whole function can get as high as we want. So that's (b, infinity)

B. ƒ(x)=3√(x-b)+a
Setting the radical to 0 gives a as the lowest possibility for the range.

C. ƒ(x)=-3√(x+a)-b
Radical to 0 gives -b as the highest possibility, since the whole radical is multiplied by a negative and will decrease the function as it increases.

D. ƒ(x)=-√(x+b)-a
Radical to 0 will give -a as the highest possibility.

Answer 5

Any chance you mistyped a negative sign in the problem somewhere? Perhaps before an a? Left one out, or else included one that should have been left out?

Answer 6

Do you own homework, Kassia