Posted by **jane** on Monday, September 3, 2012 at 8:11pm.

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

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

- precalc review/calc -
**Damon**, Monday, September 3, 2012 at 8:30pm
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

- do NOT agree with you -
**Damon**, Monday, September 3, 2012 at 8:31pm
Last sentence is a typo.

- precalc review/calc -
**jane**, Monday, September 3, 2012 at 10:34pm
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

## Answer This Question

## Related Questions

- math - questions involving domain and range... 1. Find the domain of the ...
- calcius - Determine whether the relation represents a function. If it is a ...
- Pure Mathematics - 1. Given that the straight line y=c-3x does not intersect the...
- Calculus - Find the sum and difference functions f + g and f – g for the ...
- Algebra-Please check - 1. solve sqrt (11-x) = sqrt(x-7) choices are 6,7,8 or9 I ...
- Algebra - I think this is a easy trick question, so I probably know the answer ...
- calculus - Find an expression for the function whose graph is the given curve. a...
- precalc - find the domain and range of the following as an inequality and ...
- precalculus check immediately - suppoe f is a function with domain [1,3]and ...
- Calc I - Find the range of y = (3x-1)/(2x^2 + x - 6) I was going to take the ...

More Related Questions