T2W1L2: Functions

Cambridge Methods 11: Exercises 6C - 6D

recap §

• relations
  • one to one
  • many to one
  • one to many

functions §

• what is a function?
  • a function is a relation where each element of the domain maps onto one element of the range.
  • what is considered functions?
    • one-to-one and many-to-one
  • what is not considered functions?
    • one-to-many are not functions
• does {(1,5),(1,1),(7,-2),(-5,-10)} describe a function or a relation (explain why and identify the type of function)
  • an input of 1 maps to an out of of 5 and 1 (1)
  • therefore it is a one-to-many relation (1)
  • therefore it is a relation only
• determine whether the following describe functions or relations.
  • $y=x^2+2$
    • if you rearrange the equation, then $y=\pm \sqrt{x-2}$ therefore it is a one-to-many (because of the $\pm$) (1)
    • therefore it is only a relation (not a function) (1)
• what is a vertical line test
  • if a vertical line intersects the graph no0 more than once over the entire domain, then it is a function
  • if it intersects more than once, it is not a functon
• what is a horizontal line test (not needed)
• secret tip to get higher marks
  • be detailed in your explanation