SOLUTION: How would you find the range of a function on the given domain. f(x)={{{sqrt(9-x^2)}}}, {{{-3<=x<=1}}}

Algebra ->  Functions -> SOLUTION: How would you find the range of a function on the given domain. f(x)={{{sqrt(9-x^2)}}}, {{{-3<=x<=1}}}      Log On


   

Question 503576: How would you find the range of a function on the given domain.
f(x)=sqrt%289-x%5E2%29, -3%3C=x%3C=1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The square root function is a function which increases over its entire domain (ie going from left to right, the y values increase)


So the smallest possible value in the range will result when you plug in x = -3 (the smallest value in the domain)

So plug in x = -3,

f%28x%29=sqrt%289-x%5E2%29


f%28-3%29=sqrt%289-%28-3%29%5E2%29


f%28-3%29=sqrt%289-9%29


f%28-3%29=sqrt%280%29


f%28-3%29=0


So when x = -3, y = 0. So the smallest value in the range is 0.

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Similarly, the largest value in the range will result from the largest value in the domain, which is x = 1

So plug in x = 1,

f%28x%29=sqrt%289-x%5E2%29


f%281%29=sqrt%289-%281%29%5E2%29


f%281%29=sqrt%289-1%29


f%281%29=sqrt%288%29


f%281%29=2%2Asqrt%282%29


So when x = -3, y+=+2%2Asqrt%282%29. So the largest value in the range is 2%2Asqrt%282%29

So the range is 0%3C=f%28x%29%3C=2%2Asqrt%282%29 or 0%3C=y%3C=2%2Asqrt%282%29


This means that the range in interval notation is




If you need more help, feel free to email me at jim_thompson5910@hotmail.com
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Thanks,

Jim