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Section 5.2: Relations and Functions

Section 5.2: Relations and Functions. Objectives: To identify relations and functions To find the domain and range of a relation and a function To evaluate functions. Relation : A set of ordered pairs Example : Ordered Pairs : (2, 0) (12, 1)

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Section 5.2: Relations and Functions

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  1. Section 5.2: Relations and Functions Objectives: To identify relations and functions To find the domain and range of a relation and a function To evaluate functions

  2. Relation: A set of ordered pairs Example: Ordered Pairs: (2, 0) (12, 1) (18, 1) (7, 2)

  3. Domain: Set of first coordinates of the ordered pair Range: Set of second coordinates Ordered Pairs: (2, 0), (12, 1), (18, 1), (7, 2) Domain: {2, 7, 12, 18} Range: {0, 1, 2}

  4. Example Find the domain and range of the relation represented by the data in the table. Domain: Range:

  5. Function: A relation that pairs each domain value with exactly one range value *Each x value can only correspond to ONE y value Ways to determine if a relation is a function: • Graph • Mapping

  6. Vertical Line Test If any vertical line passes through more than one point of the graph, the relation isn’t a function. Examples: Graph the ordered pairs and determine if the relation is a function by using the vertical line test. • {(3, 2), (5, -1), (-5, 3), (-2, 2)} • {(4, 3), (2, -1), (-3, -3), (2, 4)}

  7. Mapping • List the domain and range values in order. • If a number appears more than once, only write it once. • Draw lines from the domain values to their range values • If every domain value pairs up with only one range value, then the relation is a function Examples: {(-1, 2), (0, 3), (4, 3), (0, 5)} {(4, 5), (1, 0), (3, 0), (2, -2)}

  8. Function Rule • An equation that describes a function Example: y = 5x + 8 x = input y= output When given input values you can use the function rule to find the output values.

  9. y = 5x + 8 InputOutput 0 1 2

  10. Function Notation Another way to write y = 5x + 8 is f(x) = 5x + 8 • A function is in function notation when you use f(x) to indicate the outputs. • f(x) is read as “f of x” or “f is a function of x”

  11. Evaluating a Function Rule • Evaluate f(x) = -5x + 25 for x = -2 • Evaluate g(x) = 4x2 + 2 for x = 3

  12. Finding the Range • Remember: input values = domain output values = range Example: Evaluate the function f(g) = -2g + 4 to find the range for the domain {-1, 3, 5}

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