# Rational Functions and Graphs

### Graphs

###### Graphs of Rational Functions

Graph of $$y = \dfrac 1x$$

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

Graph of $$y = \dfrac {ax + b}{px + q}$$

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

Graph of $$y = \dfrac {ax^2 + bx + c}{px + q}$$

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