Functions

• If it says 11 is the image of 3 means f(x) is the image of x,so f(3)=11
• One-to-one mapping

  every value of x has one value of y
• Many-to-one

  many x values give one y
• One-to-many

  one x value gives many y values
• A function is a type of mapping where there is only one y value to each x value,so a function is a mapping that is that is one-to-one or many-to-one
• Vertical line test

  If lines only cross the curve/line once then it is a function
• Horizontal line test

  if its one-to-one only crosses once

  If it crosses more than once it is many-to-one
• limitations to a domain

  1/x+3 x can't equal -3

  log(a) a>0

  square root a a>or equal to 0
• The range of g must lie within the domain of f in order for the composite function fg to be defined
• f(x) is a reflection of f-1(x) in the line y=x
• Self-inverse functions when f(x)=f-1(x)
• The domain of f-1(x) is the same as the range of f(x) and vice versa
• when working out the inverse of a function sometimes its mapping is one-to-many meaning it is no longer a function,we limit domain to change its mapping (get rid of turning points as no t.p means it is a function)
• To prove something is a function the gradient has to be positive or 0 no turning points
• Many to one functions do not have an inverse