1.1Relations and Functions

Relations• the pairing of elements of one set to the

elements of another set• can be represented by ordered pairs– First coordinate is the domain– Second coordinate is the range

• can be represented as a table of values• can be graphed • some relations can be described by a rule or

equation that relates the first and second coordinates

• State the relation of the windchill data as a set of ordered pairs

• State the domain and range of the relation

Windchill Factors at 20⁰ F

Wind Speed(mph)

Windchill Temperature

(⁰F)

5 19

10 3

15 -5

20 -10

25 -15

30 -18

The domain of a relation is all consecutive integers between -2 and 2. The range y of the relation is 2 less than twice x, where x is a member of the domain. Write the relation as a table of values and as an equation. Then graph the relation.

x y

State the domain of range of each relation.

Functions• A function is a relation in which each element

of the domain is paired with exactly one element in the range.– The domain cannot repeat

• On a graph of a relation, if every vertical line drawn on the graph of a relation passes through no more than one point on the graph, then the relation is a function. This is called the vertical line test.

State the domain and range of each relation. Then state whether the relation is a function.

a.{(-2,0), (3,2),(4,5)}

b.{(-3,-2), (-2,-2), (-1,-2), and (0,-2)}

Determine whether the graph of each relation represents a function.

Function Notation• f(x) is read “f of x” and should be interpreted

as the value of function f at x.• The expression y = f(x) indicates that for each

element in the domain that replaces x, the function assigns one and only one replacement for y.

• The ordered pairs of a function can be written in the form (x, y) or (x, f(x)).

Evaluate each function for the given value.f(-1) if f(x) = -x³ - 1

f(3) if f(x) =

g(m) if g(x) = 2x⁶ - 10x⁴ - x² + 5

h(a-2) if h(x) = 2x² – x + 3

23x

When given the equation of a function but the domain is not specified, the domain is all real

numbers for which the corresponding values in the range are also real numbers.

Homework

pages 10 – 1118, 38, 42, 44, 46

48, and 52 a, b, cYou do not have to write the problems.

You must follow directions and show all work.