Section 4.1 Properties of functions You are expected to take notes in a bound notebook.

A blast from the past: Symbols: Symbols:

Graphs of single variable inequalities: Graphs of single variable inequalities: Click here to see examples of each. Click here to see examples of each.

What does the infinity symbol in a math class mean?

Deep and Wide: Domain & Range The student is expected to identify mathematical domains and ranges and determine reasonable domain and range values for given situations, both continuous and discrete

A function is a set of ordered pairs of numbers (x, y) such that no x –values are repeated. A function is a set of ordered pairs of numbers (x, y) such that no x –values are repeated. What are the domain and range of a function? What are the domain and range of a function? The domain and range of a function are sets that describe those ordered pairs. The domain and range of a function are sets that describe those ordered pairs.

DefinitionExample {(3, 6), (2, 8), (5, 3)} Domain All the x-coordinates in the function's ordered pairs { 3, 2, 5} Range All the y-coordinates in the function's ordered pairs { 6, 8, 3}

The domain is the set of all the values of the independent variable, the x- coordinate The range is the set of all the values of the dependent variable, the y- coordinate.

Identify the domain and range of the function below. { 2, 7), (4, 11), (6, 15), (8, 19)} The domain is { 2, 4, 6, 8} The domain is { 2, 4, 6, 8} The range is { 7, 11, 15, 19} The range is { 7, 11, 15, 19}

Graphs The domain of a function is the set of all the x-coordinates in the functions’ graph The domain of a function is the set of all the x-coordinates in the functions’ graph Domain 3 ≤ x ≤ 12

The range of a function is the set of all the y- coordinates in the functions’ graph Range 6 ≤ y ≤ 12

What is the domain of this function? What is the range of this function? Domain is 0 ≤ x ≤ 4 Range is 1 ≤ y ≤ 5

The graph shows the path of a golf ball Which of following describes the range of this function? a)0 < y < 100 b)0 ≤ y ≤ 100 c)0 ≤ x ≤ 5 d)0 < x < 5

What is the domain of this function? A -1 ≤ x ≤ 5 B -1 ≤ x ≤ 9 C 2 ≤ x ≤ 5 D 0 ≤ y ≤ 9

What is the domain of the function shown on the graph? A -2 < y ≤ 2 B -4 ≤ x ≤ 6 C -4 < y ≤ 2 D -2 < x ≤ 6

Sometimes you will be asked to determine a REASONABLE domain or range

The average daily high temperature for the month of May is represented by the function t = 0.2n + 80 t = 0.2n + 80 Where n is the date of the month. May has 31 days. What is a reasonable estimate of the domain? Answer: 1 ≤ n ≤ 31 What is a reasonable estimate of the range Answer: See next slide

Our function rule is: t = 0.2n + 80 Our domain is 1 ≤ n ≤ 31 Our smallest possible n is 1 Our largest possible n is 31 To find the range, substitute 1 into the equation and solve. Then substitute 31 into the equation and solve.

Our function rule is: t = 0.2n + 80 Substitute a 1 t = 0.2n + 80 t = 0.2(1) + 80 t = t = 80.2 Substitute a 31 t = 0.2n + 80 t = 0.2(31) + 80 t = t = 86.2 Reasonable range is 80.2 ≤ t ≤ 86.2

State the domain and range of the following function:

The Vertical Line Test The vertical line test is used to determine if a graph is a function.

If a vertical line passes through a graph more than once, the graph is not the graph of a function. Hint: Pass a pencil across the graph held vertically to represent a vertical line. The pencil crosses the graph more than once. This is not a function because there are two y-values for the same x- value.

Homework expectation: All homework is due the next class period. All homework is due the next class period. Grace period of one week is provided but you are responsible to keep track of the deadlines… there will be no reminders. Grace period of one week is provided but you are responsible to keep track of the deadlines… there will be no reminders.

On your own: Read section 4.1. Read section 4.1. Make sure your classroom notes are complete and pretty! Make sure your classroom notes are complete and pretty! Give a complete solution to the following problems: Section 4.1 page 122 Written exercises #1-11 odds and then all.