Algebra 2 Functions and Relations Flashcards

Mapping Diagrams and Functions

• A mapping diagram visually represents relationships by showing how each input corresponds to an output.
• Example relation:
  • (-2 maps to -6)
  • (0 maps to 3)
  • (1 maps to -5)
  • (5 maps to 0)

Graphing Relations

• Graph points:
  • (-1, 1/2),
  • (-1/2, -1),
  • (3/2, 0),
  • (2, 3/2)
• Domain consists of all x-values:
  • (-1, -1/2, 3/2, 2)
• Range consists of all y-values:
  • (-1, 0, 1/2, 3/2)

Identifying Functions

• A relation is not a function if an input is associated with multiple outputs.
• Example relation:
  • {(14, 15), (5, 7), (3, 10), (11, 1), (5, 8)} is not a function because the input 5 corresponds to two outputs (7 and 8).

Vertical Line Test

• A graph represents a function if any vertical line drawn intersects it at most once.
• Identifying which graph passes this test is crucial for determining functions.

Function Evaluation

• Evaluate linear functions by substituting values into the function:
  • For f(x) = 5x + 1, substituting x = -4 yields f(-4) = -19.

Cost Functions

• Functions can model real-world scenarios, like ticket pricing.
• Example function for concert tickets includes a base price and a handling fee:
  • Total cost = 25t + 1.75
  • For 6 tickets, evaluate function: Total cost = $151.75.