Asymtotes

For \(x \rightarrow \: \sim, \: y \rightarrow 0\)

Asymtote \(y = 0\)

For \(y \rightarrow \: \sim, \: x \rightarrow 0\)

Asymtote \(x = 0\)

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

Change the form of \(y = \dfrac {ax + b}{px + q}\) into \(y = m + \dfrac {t}{px + q}\)

Asymtotes

For \(x \rightarrow \: \sim, \: y \rightarrow m\)

Horizontal asymtote \(y = m\)

For \(y \rightarrow \: \sim, \: px + q \rightarrow 0\)

Vertical asymtote \(x = - \dfrac qp\)

Axis intercept

X-intercept when y = 0

Y-intercept when x = 0

Change the form of \(y = \dfrac {ax^2 + bx + c}{px + q}\) into \(y = mx + n + \dfrac {t}{px + q}\)

Asymtotes

For \(x \rightarrow \: \sim, \: y \rightarrow mx + n\)

Oblique asymtote \(y = mx + n\)

For \(y \rightarrow \: \sim, \: px + q \rightarrow 0\)

Vertical asymtote \(x = - \dfrac qp\)

Axis intercept

X-intercept when y = 0

Y-intercept when x = 0