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rock.freak667

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## Main Question or Discussion Point

I was told to sketch this graph:

[tex]y=\frac{x-1}{x^2-100}[/tex]

when x=0,y=.01

[tex]y=\frac{\frac{1}{x}-\frac{1}{x^2}}{1-\frac{100}{x^2}}[/tex]

as [itex]x \rightarrow \infty;y \rightarrow 0 \Rightarrow[/itex] y=0 (i.e. x axis is a horizontal asymptote to the curve)

BUT

when y=0; x-1=0 so that x=1. So a point on the curve is (1,0)

How can the x-axis be a horizontal asymptote to the curve yet the curve passes through (1,0)?

[tex]y=\frac{x-1}{x^2-100}[/tex]

when x=0,y=.01

[tex]y=\frac{\frac{1}{x}-\frac{1}{x^2}}{1-\frac{100}{x^2}}[/tex]

as [itex]x \rightarrow \infty;y \rightarrow 0 \Rightarrow[/itex] y=0 (i.e. x axis is a horizontal asymptote to the curve)

BUT

when y=0; x-1=0 so that x=1. So a point on the curve is (1,0)

How can the x-axis be a horizontal asymptote to the curve yet the curve passes through (1,0)?