2-1 Relations and Functions2-2 Direct Variation

Algebra II Chapter 2 Functions, Equations, and Graphs

Essential Understanding and Objectives

Essential Understanding: a pairing of items from tow sets is special if each item from one set pairs exactly with one item from the second set.

Essential Understanding: some quantities are in a relationship where the ratio of corresponding values is constant

Objectives: Students will be able to graph relations Students will be able to identify functions Students will be able to write and interpret direct

variation equations

Iowa Core Curriculum

Functions – (Review) F-IF.1. Understand that a function from one set

(called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

F-IF.2. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

Iowa Core Curriculum

Algebra A-CED.2. Create equations in two or more variables to

represent relationships between quantities; graph equations on coordinate axes with labels and scales.

Functions F-IF.1. Understand that a function from one set (called the

domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

F-BF.1. Write a function that describes a relationship between two quantities.★ Determine an explicit expression, a recursive process, or steps for calculation from a context.

Relations

Set of pairs of input and output values

Represented in four different ways Ordered Pair Mapping

Diagram Table of Values Graph

Example

The monthly average water temperature of the Gulf of Mexico in Key west, Florida varies during the year. In January, the average temperature is 69 degrees, in February, 70 degrees, in March, 75 degrees, and in April, 78 degrees. How can you represent this relation?

Domain and Range

What is domain? Input values of a relation/function (x-

coordinates) What is range?

Output values of a relation/function (y-coordinates)

What is the domain and range of the relation? {(-3, 14), (0, 7), (2, 0), (9, -18), (23, -99)}

Functions

A relation in which each element of the domain corresponds with exactly one element of the range.

Vertical Line Test

On a graph you can use the vertical line test to determine if the relation is a function.

Vocabulary

Function Rule: an equation that represents an output value in terms on an input value

Function Notation: uses f(x) = equation

Independent Variable: x, represents the input of a function

Dependent Variable: f(x) or y, represents the output of a function

For f(x) = -4(x) + 1, what is the output for the given inputs: -2, 0, and 5?

Word Problem

A pizza costs $14; the flat delivery fee is $1.50. What function rule models the total cost of the number of pizzas delivered. Evaluate for 5 pizzas.

Homework

Pg. 64 #1 – 26 all, 32, 3428 problems