Rational Function Domain Interval Notation

Discontinuous Graph

x-intercept

Rational Function

Continuous Graph

Domain

Range

Interval Notation

Piecewise Function

Quadratic

Cubic

Linear

Rational

$$x\ne1$$  

$$x\ne3$$  

$$y\ne1$$  

$$y\ne3$$  

$$x\ge1$$  

(-∞,-1) U (-1,5) U (5,∞)

(-∞,-1) U (5,∞)

(-∞,∞)

(-∞,-3) U (-3,-1) U (-1,2) U (2,5) U (5,∞)

(-∞,-5) U (-5,1) U (1,∞)

(-∞,-5) U (5,∞)

(-∞,7) U (7,19) U (19,∞)

(-∞,-1) U (-1,5) U (5,∞)

(-∞,-1) U (5,∞)

(-∞,∞)

(-∞,-3) U (-3,-1) U (-1,2) U (2,5) U (5,∞)

(-∞,-5) U (-5,1) U (1,∞)

(-∞,-5) U (5,∞)

(-∞,7) U (7,19) U (19,∞)

(3, ∞)

[-3, ∞)

(-∞, 4]

(-∞, 4)

$$x\ne1$$  

$$x\ne3$$  

$$y\ne1$$  

$$y\ne3$$  

$$x\ge1$$  

$$x=-1,\ x=1$$  

$$x\ne-1,\ x\ne1$$  

$$\left(-\infty,\ -1\right)\cup\left(1,\ +\infty\right)$$  

$$\left(-\infty,\ -1\right)\cup\left(-1,\ 1\right)\cup\left(1,\ +\infty\right)$$