Deep and Wide: Domain & Range

Slides:

Advertisements

Similar presentations

Algebra I End-of-Course Exam Changing the way we teach.

Advertisements

Both finite sets, A and B, are relations. A= { (0,2), (1,3), (2,4) }

 Function  Coordinate System  Y-Axis  X-Axis  Origin  Ordered Pair  X-Coordinate  Y-Coordinate  Independent Variable  Dependent.

Algebra 1 Seminar Domain and Range Notes Vocabulary ● Domain – The domain is the set of all x-coordinates in a set of ordered pairs. ● Range – The range.

2.1 Domain and Range. Vocabulary ● Relation – A relation is a general term for any set of ordered pairs. ● Function – A function is a special type of.

Table of Contents Function: Domain and Range A function is a correspondence between two sets governed by some rule(s) such that each member of the first.

COORDINATE PLANE x-axisy-axis. COORDINATE PLANE QUADRANTS III III IV (+, +)(-, +) (-, -)(+, -)

Give an example of an ordered pair (take a guess if you don’t know).

Write and graph a direct variation equation

Thinking Mathematically Algebra: Graphs, Functions and Linear Systems 7.3 Systems of Linear Equations In Two Variables.

Functions. A function is a relation that has exactly one output for each input.

Copyright © Cengage Learning. All rights reserved.

Graph quadratic functions.

Section 2.1 – Relations and Functions You can use mappings to describe relationships between sets of numbers. A pairing of items from two sets is special.

Graphing Linear Equations Section 1.2. Lehmann, Intermediate Algebra, 3ed Section 1.2 Consider the equation. Let’s find y when So, when, which can be.

Do Now 10/26/10 In your notebook, explain how you know a function is a function. Then answer if the following three tables are functions or not. x

4.4 Equations as Relations

 If given the slope of a line and a point on it, writing an equation for the line in point slope form, is very straight forward.  Simply substitute.

Splash Screen. Lesson Menu Five-Minute Check (over Chapter 1) CCSS Then/Now New Vocabulary Key Concept: Functions Example 1:Domain and Range Key Concept:

Identifying Relations and Functions A relation is a set of ordered pairs. The domain of the relation is x-coordinate of the ordered pair. It is also considered.

Section 2.3 Notes: Rate of Change and Slope. Rate of change is a ratio that compares how much one quantity changes, on average, relative to the change.

Splash Screen. Lesson 9 MI/Vocab function coordinate system y-axis origin x-axis ordered pair x-coordinate y-coordinate Interpret graphs of functions.

Solving Polynomial Equations in Factored Form Lesson 10.4A Algebra 2.

7.6 Phase Shift; Sinusoidal Curve Fitting

Relations and Functions. Review A relation between two variables x and y is a set of ordered pairs An ordered pair consist of a x and y-coordinate A relation.

Lesson 1-8 Graphs and Functions. Definitions Functions- a relationship between input and output. Coordinate system- formed by the intersection of two.

Copyright © 2015, 2008, 2011 Pearson Education, Inc. Section 1.6, Slide 1 Chapter 1 Linear Equations and Linear Functions.

MATH II – Math I review

2.1 “Relations & Functions” Relation: a set of ordered pairs. Function: a relation where the domain (“x” value) does NOT repeat. Domain: “x” values Range:

EquationsFunctionsInequalities Domain & Range Polynomials.

LESSON 7.4 Function Notation To learn function notation To evaluate functions by substitution, by using the graphs drawn by hand, and on the graphing calculator.

P.O.D. Write the slope-intercept forms of the equations of the lines through the given point (2,1) & a)Parallel & b)Perpendicular to the line 4x – 2y =

Unit 1 VOCABULARY Standards: MCC9-12.N.Q.1-3 MCC9-12.A.SSE.1a-b MCC9-12.A.CED.1-4.

Warm-Up Determine the coordinates of each point in the graph below. y

LESSON 1–6 Relations. Over Lesson 1–5 5-Minute Check 1 What is the solution of 5b – 11 = 34 given the replacement set {7, 9, 13, 16, 22}?

1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 9-1 Exponential and Logarithmic Functions Chapter 9.

Warm Up Solve each equation for y. 1.x = -4y 2.x = 2y x = (y + 3)/3 4.x = -1/3 (y + 1)

Section 3.4 Solving Systems of Linear Equations in Two Variables by the Substitution Method.

Solving Systems by Elimination 5.4 NOTES, DATE ____________.

Domain: a set of first elements in a relation (all of the x values). These are also called the independent variable. Range: The second elements in a relation.

Notes 6.5, Date__________ (Substitution). To solve using Substitution: 1.Solve one equation for one variable (choose the variable with a coefficient of.

3.2 Relations And Functions. A relation is a set of ordered pairs. {(2,3), (-1,5), (4,-2), (9,9), (0,-6)} This is a relation The domain is the set of.

Unit 4 - Relations and Functions 1 Relations and Functions MGSE8.F.1 Understand that a function is a rule that assigns to each input exactly one output.

Goal: Identify and graph functions..  Relation: mapping or pairing, of input values with output values.  Domain: Set of input values.  Range: set of.

CCSS Content Standards F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of.

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

Section 4.2.  Label the quadrants on the graphic organizer  Identify the x-coordinate in the point (-5, -7)

Algebra 2 Foundations, pg 64  Students will be able to graph relations and identify functions. Focus Question What are relations and when is a relation.

Topic 4 Functions Graphs’ key features: Domain and Range Intercepts

Ch 2ABC 2A: Relations and Functions 2B: Function Notation 2C: Domain and Range.

Functions and relations

Topic 4 Functions Date: August 21, 2017

Relations and Functions Pages

Linear Functions SOL 8.14, SOL 8.16, SOL 8.17.

Functions and relations

Domain & Range from Graphs

Warm - Up Graph each equations on its own coordinate plane.

Solve a system of linear equation in two variables

Functions A function is a relation in which each element of the domain is paired with exactly one element of the range. Another way of saying it is that.

Deep and Wide: Domain & Range

1. b. Identify the independent and dependent variables of the given word problem. c. Is this a function or non function; why? a.

Objectives Identify solutions of linear equations in two variables.

RELATIONS & FUNCTIONS CHAPTER 4.

UNIT SELF-TEST QUESTIONS

Dependent Axis Y Answer Output Range f (x) Function Notation

Name the quadrant or the axis on which the following points lie.

Warm-up: Solve each equation for a. 1. 2a–b = 3c

Presentation transcript:

Deep and Wide: Domain & Range TEKS A.2B 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. What are the domain and range of a function? The domain and range of a function are sets that describe those ordered pairs.

Definition Example {(3, 6), (2, 8), (5, 3)} { 3, 2, 5} { 6, 8, 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 range is { 7, 11, 15, 19}

Graphs 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 Answer: Domain is 0 ≤ x ≤ 4 Range is 1 ≤ y ≤ 5

The graph shows the path of a golf ball What is the range of this function? F 0 < y < 100 G 0 ≤ y ≤ 100 H 0 ≤ x ≤ 5 J 0 ≤ x ≤ 5 Answer is G Is this function continuous or discrete? Would it be reasonable to have a range with negative numbers?

What is the domain of this function? A -1 ≤ x ≤ 5 B -1 ≤ x ≤ 9 C 2 ≤ x ≤ 5 D 0 ≤ y ≤ 9 Students should immediately realize that “D” cannot be the answer because y is the dependent variable and therefore y represents the RANGE, not the DOMAIN. Answer is A

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 Students should immediately realize that A and C cannot be the answer. We are looking for domain. Therefore, our variable will be an X, NOT A Y.

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 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 = 0.2 + 80 t = 80.2 Substitute a 31 t = 0.2n + 80 t = 0.2(31) + 80 t = 6.2 + 80 t = 86.2 Reasonable range is 80.2 ≤ t ≤ 86.2