1. 5.2 Relations and Functions A relation is a set of ordered pairs. The domain of a relation is the set of first coordinates of the ordered pairs – the x- coordinates. The range of a relation is the set of second coordinates – the y-coordinates.

2. Finding Domain and Range Find the domain and range of the ordered pairs listed for the giraffe data. (18, 4.25) (20, 4.40) (21, 5.25) (14, 5.00) (18, 4.85) Domain: {14, 18, 20, 21} Range: {4.25, 4.40, 4.85, 5.00, 5.25} Age (years) Height (meters) 184.25 204.40 215.25 145.00 184.85 Giraffes AgeHeight

3. Function A function is a relation that assigns exactly one value in the range to each value in the domain. –You can tell if a relation is a function by analyzing the graph of a relation using the vertical-line test. If any vertical line passes through more than one point of the graph, the relation is not a function.

4. Using the Vertical-Line Test Determine whether the relation {(3, 0), (-2, 1), (0, -1), (-3, 2), (3, 2)} is a function. Step 1 – graph the ordered pairs on a coordinate plane.

5. Vertical-Line Test Step 2 – use the Vertical – Line test. A vertical line passes through both (3, 0) and (3, 2), so the relation is not a function.

6. Using a Mapping Diagram Determine whether each relation is a function. a. {(11, -2), (12, -1), (13, -2), (20, 7)} DomainRange 11 -2 12 -1 13 7 20 There is no value in the domain that corresponds to more than one value of the range. The relation is a function.

7. Using a Mapping Diagram Determine whether each relation is a function. b. {(-2, -1), (-1, 0), (6, 3), (-2, 1)} DomainRange -2 -1 -1 0 6 1 3 The domain value corresponds to two range values -1 and 1. The relation is not a function.

8. Evaluating Functions A function rule is an equation that describes a function. –The domain is the set of input values. –The range is the set of output values. A function is in function notation when you use f(x) to indicate the outputs. –You read f(x) as “f of x” or “f is a function of x”. –The notations g(x) and h(x) also indicate functions of x.

9. Evaluating a Function Rule a.Evaluate f(n) = -3n – 10 for n = 6. f (n) = -3n – 10 f (6) = -3(6) – 10 f (6) = -18 – 10 f (6) = -28 b.Evaluate y = -2x 2 + 7 for x = -4 y = -2(-4) 2 + 7 y = -2(16) + 7 y = -32 + 7 y = -25

10. Finding the Range Evaluate the function rule f(a) = -3a + 5 to find the range of the function for the domain {-3, 1, 4}. a. f(a) = -3a + 5 f(-3) = -3(-3) + 5 f(-3) = 14 b. f(a) = -3a + 5 f(1) = -3(1) + 5 f(1) = 2 c. f(a) = -3a + 5 f(4) = -3(4) + 5 f(4) = -7

11. More Practice!!! Textbook – p. 244 #2 – 26 even.