Recording-2025-07-15T15:42:22.181Z

Function Basics

• A relation is a function iff every input x maps to exactly one output y.
• Core memory aid: “Look at x; x can’t repeat.”

Determining “Function‐ness” From Ordered Pairs

• Scan the list of ordered pairs.
  • Any duplicate x‐values ⇒ NOT a function.
• Example set: (3,-2),(4,1),(4,8),(4,9)
  • Duplicate x=4 appears ⇒ not a function.
• Even if not a function you can still list:
  • Domain = all unique x’s → {3,4}
  • Range = all y’s → {-2,1,8,9}

Determining From an Equation

• Check the exponent on y (or see if y is explicitly solved).
  • If y is to the first power (e.g. y = 2x+5) ⇒ generally a function.
  • Higher even powers of y (e.g. y^2 = x) usually fail the Vertical Line Test.

Vertical