For a warm up in my math class we were told to find the exact domain and exact range for the following function:

[math]y=\frac{-1}{15\sqrt{36-x^{2}}}[/math]

 

Find the domain of [math]\left(-6,6\right)[/math] easily. However the range was harder to find. I realized that the upper range is going to be:

[math]\frac{-1}{15\sqrt{36-0^{2}}}=\frac{-1}{90}[/math].

It's the lowest value that I am struggling to find. I think it might be negative infinity because as x approaches 6 I will get -1 over 15 times the square root of a ridiculously small number, which will be a huge negative number. However I am not sure can anyone point me in the right direction.

You are right with minus infinity.

 

Using calculus you can examine the limits (being careful about the direction) as [math]x \rightarrow \pm 6[/math]. However, this seems a little more advanced that you need.

 

Try plotting the function and see if that fits in with your initial thoughts.