How do you graph $f\left(x\right)=\frac{x}{x-2}$ using holes, vertical and horizontal asymptotes, x and y intercepts?

blogswput
2022-09-12
Answered

How do you graph $f\left(x\right)=\frac{x}{x-2}$ using holes, vertical and horizontal asymptotes, x and y intercepts?

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Let$\varphi :P{P}^{1}\to {\mathrm{\forall}}^{1}$ be a rational function. Since $\mathrm{\forall}}^{1}\subset P{P}^{1$ we can think $\varphi :P{P}^{1}\to P{P}^{1}$ as rational function. As every rational map from $P{P}^{1}\to P{P}^{n}$ is regular, so $\varphi$ is regular. We also know that any regular function on $P{P}^{1}$ is constant, so $\varphi$ is constant.

Let

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