For the curve y=2^[sqrt(9-x2)], find the range of the function.

Question

I think the range is [0,8] but I don't know why. Could you show me how to get to that answer? Thanks.

Answer 1

I assume you mean:

y=2^[sqrt(9-x^2)]

we do not want to take the sqrt of a negative number so domain is |x|<3
or
-3 < x < +3
eg
if x = -3 or + 3, y = 2^0 = 1
if x = -1 or + 1, y = 2^sqrt 8 = 7.1
if x = -2 or + 2, y = 2^sqrt 5 = 4.7
if x = 0 , y = 2^3 = 8
So
I think the range of y is 1 to 8, not 0 to 8
that corresponds to y between 0 and 8 so I agree with you

Answer 2

Last sentence is a typo.

Answer 3

Thanks! So because the smallest and biggest numbers +/- 3 and the middle number 0 result in the smallest and largest y values, 1 and 8 respectively, the range is therefore [1, 8]. That makes sense. :D