1. 1.1 Relations and Functions

2. 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

3. Windchill Factors at 20⁰ F
Wind Speed
(mph)
Windchill
Temperature (⁰F) 5 19 10 3 15 -5 20
-10 25
-15 30
-18
State the relation of the windchill data as a set of ordered pairs
State the domain and range of the relation

4. The domain of a relation is all consecutive integers between -2 and 2
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

5. State the domain of range of each relation.

6. 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.

7. {(-3,-2), (-2,-2), (-1,-2), and (0,-2)}
State the domain and range of each relation. Then state whether the relation is a function.
{(-2,0), (3,2),(4,5)}
{(-3,-2), (-2,-2), (-1,-2), and (0,-2)}

8. Determine whether the graph of each relation represents a function.

9. 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)).

10. 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

11. 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.

13. Homework
pages 10 – 11 18, 38, 42, 44, 46 48, and 52 a, b, c You do not have to write the problems. You must follow directions and show all work.