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I am trying to find and graph the level curve [tex]f(x,y)=\sqrt{x^2-1}[/tex] that passes throught the point [tex](0,1)[/tex], as well as its domain and range.

I am not sure if my reasoning is right, so let me know if I got the wrong idea.

For the graph I have [tex]x = 1[/tex] which is independent of y and is just a vertical line. Is this correct?

Would the domain be [tex](-\infty, -1]\cup[1,\infty)[/tex] or [tex][1,\infty)[/tex] ? Because [tex]\sqrt{x^2-1} = \sqrt{x-1}\sqrt{x+1}[/tex]

I'm confused.

Range: [tex][0,\infty)[/tex]

any help would be greatly appreciated

Thanks

Update: this a function of two variables

I am not sure if my reasoning is right, so let me know if I got the wrong idea.

For the graph I have [tex]x = 1[/tex] which is independent of y and is just a vertical line. Is this correct?

Would the domain be [tex](-\infty, -1]\cup[1,\infty)[/tex] or [tex][1,\infty)[/tex] ? Because [tex]\sqrt{x^2-1} = \sqrt{x-1}\sqrt{x+1}[/tex]

I'm confused.

Range: [tex][0,\infty)[/tex]

any help would be greatly appreciated

Thanks

Update: this a function of two variables

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