Asymtotes

For $x\to \sim ,y\to 0$

Asymtote $y=0$

For $y\to \sim ,x\to 0$

Asymtote $x=0$

The curve does not cut x-axis and y-axis

Change the form of $y={\displaystyle \frac{ax+b}{px+q}}$ into $y=m+{\displaystyle \frac{t}{px+q}}$

Asymtotes

For $x\to \sim ,y\to m$

Horizontal asymtote $y=m$

For $y\to \sim ,px+q\to 0$

Vertical asymtote $x=-{\displaystyle \frac{q}{p}}$

Axis intercept

X-intercept when y = 0

Y-intercept when x = 0

Change the form of $y={\displaystyle \frac{a{x}^2+bx+c}{px+q}}$ into $y=mx+n+{\displaystyle \frac{t}{px+q}}$

Asymtotes

For $x\to \sim ,y\to mx+n$

Oblique asymtote $y=mx+n$

For $y\to \sim ,px+q\to 0$

Vertical asymtote $x=-{\displaystyle \frac{q}{p}}$

Axis intercept

X-intercept when y = 0

Y-intercept when x = 0