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find domain and range of the following a. x^2+y^2=16
b. f(x)=root(9-x^2)
c. f(x)=root(x^2-9)

Answer 1

a)$x^2+y^2=16$ is the equation of a circle with centre $(0,0)$ and radius $\sqrt{16}=4$.
Plot it into a graph, and notice $-4\le x\le4$ and $-4\le y\le4$. So, 
$Domain=[-4,4]\\Range=[-4,4]$
b)Let
$y=f(x)=\sqrt{9-x^2}:y\ge0\\\Rightarrow x^2+y^2=9$
This is again the equation of a circle with centre $(0,0)$ and radius $\sqrt{9}=3$
Plot it into a graph and notice $-3\le x\le3$ and $0\le y\le3$ ($y\ge0$ as stated above).
So, 
$Domain=[-4,4]\\Range=[0,4]$
c)Let
$y=f(x)=\sqrt{x^2-9}:y\ge0\\\Rightarrow x^2-y^2=9$
This is again the equation of a hyperbola with centre $(0,0)$ and X-intercepts $(3,0)$ and $(-3,0)$.
Plot it into a graph and notice $3\le |x|\le\infty$ and $0\le y\le\infty$ ($y\ge0$ as stated above).
So, 
$Domain=(-\infty,-3]\cup[3,\infty)\\Range=[0,\infty)$