Set of first coordinates in an ordered pair. (the x values) Range: Section 5-2 Relations and Functions SPI 23C: determine the domain/range of a function represented by the graph of real-world situations Objectives: Identify relations and functions Evaluate Functions Vocabulary Domain: Set of first coordinates in an ordered pair. (the x values) Range: Set of second coordinates in a ordered pair (the y values) Relation: Set of all ordered pairs; x value may be repeated Function f(x) or y: a relation that assigns exactly one value in the range to each value in the domain. (x value may not be repeated)

Write values from table as an ordered pair Domain and Range Giraffes Age (years Height (meters) 18 4.25 20 4.40 21 5.25 14 5.00 4.85 Write values from table as an ordered pair Domain Range Domain Age Height Range (18, 4.25) (20, 4.40) (21, 5.25) (14, 5.00) (18, 4.85) Domain Range x-values in a table or ordered pair write values only once in order from least to greatest D={14, 18, 20, 21} y-values in a table or ordered pair write values only once in order from least to greatest R={4.25, 4.40, 4.85, 5.00, 5.25}

Relation and Functions Giraffes Age (years Height (meters) 18 4.25 20 4.40 21 5.25 14 5.00 4.85 Not a Function (x-value is repeated) Relation Function Set of all ordered pairs x-value may be repeated The (age, height) ordered pair form a relation. A special relation x-value may not be repeated The (age, height) ordered pair does NOT form a relation.

Determine if a Relation is a Function (Vertical Line Test) Use to determine if a relation is a function Plot the data from a table of values, on a coordinate plane. x-values (Domain) y-values (Range) 3 -2 1 -1 -3 2 Pass a pencil, vertically, across the graph. If it passes through only one point at a time, then it is a function.

Vertical Line Test Example: Use the vertical line test to determine if the graph represents a function.

Vertical Line Test Example: Does the graph represent a function? Yes, because it passes the vertical line test since the touches only 1 point at a time.

Vertical Line Test Example 2: Use the vertical line test to determine if the graph represents a function.

Vertical Line Test Example 2: Does the graph represent a function? No, because it fails the vertical line test since the touches more than 1 point at a time.

Determine if a Relation is a Function (Mapping Diagram) Also used to determine if a relation is a function The relation is NOT a function List domain and range values in order x-values (Domain) y-values (Range) 3 -2 1 -1 -3 2 Domain Range -3 -2 3 -2 -1 1 2 Draw arrow from domain values to corresponding range values Notice the domain value 3 corresponds to 2 range values

Determine if a Relation is a Function (Mapping Diagram) Which mapping diagram is a function? 11 12 13 20 Domain -2 -1 7 Range -2 -1 4 Domain 1 3 Range This is a function This is NOT a function

Investigate Functions The Function Machine INPUT (domain, x value) Domain (x value) Range (y value) x = 0 4 Function rule f(x) = 2x + 4 y = 2x + 4 1 6 f(1) = 2(1) + 4 f(0) = 2(0) + 4 x = 1 Output (range, y value) f(1) = 6 f(0)= 4 Each x value has one and only one y value.

Do Now A Little Practice 1. Evaluate the function rules: 1. f(n) = -3n – 10 for n = 6 2. y = -2x2 + 7 for x = - 4 2. What is the range of the function in problem 1 for the domain {0, 1, 2}? f(6) = -3(6) – 10 = -18 – 10 = -28 y = -3(-4)2 + 7 = -3(16) + 7 = -41 f(0) = -3(0) – 10 = 0 – 10 = -10 f(1) = -3(1) – 10 = -3 – 10 = -13 f(2) = -3(2) – 10 = -6 – 10 = -16 The range is {-16, -13, -10}.