Algebra II Relations and Functions

VOCABULARY 1. For every input of a function there is exactly/at least/at most one output.

VOCABULARY

RELATION {(0,1), (2,3), (0,4)} Input (domain) Output (range)

Circle the output values in the relation. {(1,0), (-2,3),(3,2), (5, -4)}

Write the domain of the relation. {(-2,3), (-2,1), (5, 4)}

There are 4 different ways to represent a relation:  1.______________  2.______________  3.______________  4.______________

Representing a Relation

Mapping Diagram Jan. ____ 69 ____

Ordered pairs {(Jan., 69), (Feb., ___), (____, ___), (____, ___)}

Table x (Month) Jan.69

Graph

What is the domain and range of this relation? {(-3, 14), (0, 7), (2, 0), (9, -18), (23, -99)} Domain: { } Range: { } First the set of x- coordinates: Then the set of y- coordinates:

The set of x-coordinates is the ________ of the relation. The set of y-coordinates is the ________ of the relation.

Identifying Functions Circle the range values that correspond to domain value 2. DomainRange

True or False? Every element of the input corresponds to exactly one element of the range. ______

True or False? The relation is a function. _____ DomainRange

Vertical line test A relation is a function if it can pass the vertical line test. Which means when the relation is on a graph you can not draw a straight vertical line and touch more than one point.

Use the vertical line test. Which graph(s) represent(s) a function? ______

Underline the correct word(s) to complete the sentence. If a vertical line passes through more than one point on a graph, the graph represents/does not represent a function.

Function Notation

Substitute the input into the function rule and simplify:

Writing and Evaluating a Function You are buying bottles of a sports drink mix for a softball team. Each bottle costs $1.19. What function rule models the total cost of a purchase? Evaluate the function for 15 bottles.

Writing and Evaluating a Function You are buying bottles of a sports drink mix for a softball team. Each bottle costs $1.19. What function rule models the total cost of a purchase? Evaluate the function for 15 bottles. Let c = ?. Circle your choice. cost per bottlecost of 15 bottles number of bottles boughttotal cost

Writing and Evaluating a Function You are buying bottles of a sports drink mix for a softball team. Each bottle costs $1.19. What function rule models the total cost of a purchase? Evaluate the function for 15 bottles.

Writing and Evaluating a Function You are buying bottles of a sports drink mix for a softball team. Each bottle costs $1.19. What function rule models the total cost of a purchase? Evaluate the function for 15 bottles. Relate: __________ is ___________ times _____________________

Writing and Evaluating a Function You are buying bottles of a sports drink mix for a softball team. Each bottle costs $1.19. What function rule models the total cost of a purchase? Evaluate the function for 15 bottles.

Lesson Check Error Analysis: Your friend writes, “In a function, every vertical line must intersect the graph in exactly one point.” Explain your best friends error and rewrite his statement so that it is correct.

Lesson Check Draw a vertical line on each graph that does not intersect the function.

Lesson Check Error Analysis: Your friend writes, “In a function, every vertical line must intersect the graph in exactly one point.” Explain your best friends error and rewrite his statement so that it is correct. In a function, a vertical line ____________________________________ ___________________________________.

Math Success Check off the vocabulary words you understand. □relation□function□domain□range Rate how well you can represent and interpret functions NEED TO REVIEW NOW I GET IT!