1. 2.1 Relations and Functions A relation is a set of pairs of input and output values. – There are four different ways to represent relations.

2. Domain and Range The domain of a relation is the set of inputs, also called x-coordinates, of the ordered pairs. The range is the set of outputs, also called y- coordinates, of the ordered pairs. A function is a relation in which each element of the domain corresponds with exactly one element of the range.

3. Identifying Functions Is the relation a function? Each element in the domain corresponds with exactly one element in the range. This relation is a function.

4. Identifying Functions Is the relation a function? {(4, -1), (8, 6), (1, -1), (6, 6), (4, 1)} Each x-coordinate must correspond to only one y- coordinate. The x-coordinate 4 corresponds to -1 and 1. The relation is not a function.

5. Vertical-Line Test You can use the vertical-line test to determine whether a relation is a function. The vertical-line test states that if a vertical line passes through more than one point on the graph of a relation, then the relation is not a function. If a vertical line passes through a graph at more than one point, there is more than one value in the range that corresponds to one value in the domain.

6. Using the Vertical-Line Test Use the vertical-line test. Which graph(s) represent functions? Graphs A and C fail the vertical-line test because for each graph, a vertical line passes through more than one point. They do not represent functions. Graph B does not fail the vertical-line test so it represents a function.

7. Functions A function rule is an equation that represents an output value in terms of an input value. You can write a function rule in function notation. The independent variable, x, represents the input of the function. The dependent variable, f(x), represents the output of the function. It is called the dependent variable because its value depends on the input value.

8. Using Function Notation For f(x) = -2x + 5, what is the output of the input, -3, 0, ¼ ? f(x) = -2x + 5 f(-3) = -2(-3) + 5 = 6 + 5 = 11 f(0) = -2(0) + 5 = 0 + 5 = 5 f(1/4) = -2(1/4) + 5 = -1/2 + 5 = 4.5

9. Writing and Evaluating a Function Tickets to a concert are available online for $35 each plus a handling fee of $2.50. The total cost is a function of the number of tickets bought. What function rule models the cost of the concert tickets? Evaluate the function for 4 tickets. Let t = the number of tickets bought Let C(t) = the total cost C(t) = 35t + 2.50 C(4) = 35(4) + 2.50 = 142.50 The cost of 4 tickets is $142.50.

10. More Practice!!!!! Homework – textbook p. 65 #8 – 26.