functions

• • one to one = each input has a unique input
  • many to one = each input has just one associated output but there are some inputs mapped to the same output
  • one to many = there exist inputs that are mapped to more than one output
• modulus

  • y = |f(x)| (all inside) the function will never output a negative number, all values above the x axis
  • y = f(|x|) (inputs only) all inputs are positive. the graph will be reflected in the y axis