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Understanding Relations and Functions: Key Concepts and Examples

This section covers essential vocabulary and concepts regarding relations and functions. A relation pairs input and output values, while a function ensures each input has exactly one output. The vertical line test is used to determine if a relation is a function by checking for intersections on a graph. Additionally, ordered pairs (x, y) are solutions for equations in two variables. The content includes examples of representing relations, identifying functions, graphing equations, and evaluating functions, particularly linear functions in the form y = mx + b.

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Understanding Relations and Functions: Key Concepts and Examples

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  1. 2.3 (M2) Warm Up Do # 35-38 on pg. 13

  2. 2.3 (M2) Represent Relations & Functions

  3. Vocabulary . . . • A relation is a mapping, or pairing, of input values with output values. • A function is a relation for which each input value has exactly one output value. By the vertical line test a relation is a function if and only if no vertical line intersects the graph of the relation at more than one point.

  4. An ordered pair (x,y) is a solution of an equation in two variables if substituting x and y into the equation produces a true statement. • A function is one-to-one if no two values in the domain have the same value in the range.

  5. Example 1: Represent relations and identify functions & Example 2: Graph an equation in two variables • Let’s look at the examples (1 & 2) on pg. 33 & 34 . . .

  6. Example 3: Classify and evaluate functions • Linear functions are in the form y = mx + b • Evaluate a function means to substitute in an x value and simplify • Look at example 3 on pg. 34

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