Function: An expression containing atleast one variable, where every input produces one output. Every function has unique properties and this page will list and explain them.
Vertical Line Test: If a vertical line over the graph of a function passes through only one point, the expression is a function.
Vertical Line Test: If a vertical line over the graph of a function passes through only one point, the expression is a function.
Linear Functions:
f(x)=x
Domain: (-inf, inf)
Range: (-inf, inf)
Zero: (0,0)
Symmetry: origin symmetry, over y=-x
Even or Odd: odd
Periodic: no
One-to-One: yes
Discontinuities: none
Quadratic Functions:
f(x)=x^2
Domain: (-inf, inf)
Range: [0, inf)
Zero: (0,0)
Symmetry: y-axis symmetry
Even or Odd: even
Periodic: no
One-to-one: no
Discontinuities: none
Cubic Functions:
f(x)=x^3
f(x)=x^3
Domain: (-inf, inf)
Range: (-inf, inf)
Zero: (0,0)
Symmetry: origin symmetry
Even or Odd: odd
Periodic: no
One-to one: yes
Discontinuities: none
Absolute Value Functions:
f(x)=lxl
f(x)=lxl
Domain: (-inf, inf)
Range: [0, inf)
Zero: (0,0)
Symmetry: y-axis symmetry
Even or Odd: even
Periodic: no
One-to-one: no
Discontinuities: none
Square Root Functions:
f(x)= √x
Domain: [0, inf)
Range: [0, inf)
Zero: (0,0)
Symmetry: none
Even or Odd: neither
Periodic: no
One-to-one: yes
Discontinuities: none
Reciprocal Functions:
f(x)=1/x
Domain: (-inf, 0), (0, inf)
Range: (-inf, 0), (0, inf)
Zero: none
Symmetry: origin symmetry
Even or Odd: odd
Periodic: none
One-to-one: yes
Discontinuity: infinite discontinuity
Range: (-inf, 0), (0, inf)
Zero: none
Symmetry: origin symmetry
Even or Odd: odd
Periodic: none
One-to-one: yes
Discontinuity: infinite discontinuity
- Sine Functions:
Domain: (-inf, inf)
Range: (-1, 1)
Zero: multiples of pi
Symmetry: origin symmetry
Even or Odd: odd
Periodic: 2π
One-to-one: no
Discontinuity: none
Cosine Functions:
f(x)=cos(x)
Domain: (-inf, inf)
Range: (-1,1)
Zero: multiples of (1/2)π
Symmetry: y-axis symmetry
Even or Odd: even
Periodic: 2π
One-to-one: no
Discontinuity: none
Exponential Functions:
f(x)=e^x
Domain: (-inf, inf)
Range: (0, inf)
Zero: none
Symmetry: none
Even or Odd: neither
Periodic: no
One-to-one: yes
Discontinuity: none
Natural Logarithm Functions:
f(x)=ln(x)
f(x)=ln(x)
Domain: (0, inf)
Range: (-inf, inf)
Zero: (1, 0)
Symmetry: none
Even or Odd: neither
Periodic: no
One-to-one: yes
Discontinuity: none