DO NOW – Summarize the steps you would take to solve limits. For example: – When do you factor, expand, plug in, rationalize, etc.? – What is the difference.

Slides:



Advertisements
Similar presentations
Special Functions Objective: Write and graph piecewise and absolute value functions.
Advertisements

Algebra II Piecewise Functions Edited by Mrs. Harlow.
Name:__________ warm-up 2-6 Which scatter plot represents the data shown in the table? Which prediction equation represents the data shown in the table?
Warm-Up Exercises 1. Solve |x – 6| = Solve |x + 5| – 8 = 2. ANSWER 2, 10 ANSWER –15, 5 3. A frame will hold photographs that are 5 inches by 8 inches.
• Write an inequality that describes your goal in terms of x and y.
Objective: To graph linear inequalities in two variables.
EXAMPLE 6 Solve a multi-step problem Job Earnings You have two summer jobs at a youth center. You earn $8 per hour teaching basketball and $10 per hour.
Families of Functions, Piecewise, and Transformations.
ACT Class Opener: om/coord_1213_f016.htm om/coord_1213_f016.htm
Graphing Piecewise Functions
The Beginnings of Algebra Solving Equations Graphing Linear Equations Writing Linear Equations Linear Inequalities
Warm-Up/Activator Sketch a graph you would describe as continuous.
 $10.65 x 40 = $  $ x 50 = $21,
Piecewise Functions Objective: Students will be able to graph, write and evaluate piecewise functions.
1 What you will learn today 1. How to evaluate piecewise functions 2. How to graph piecewise functions 3. How to determine piecewise functions from a graph.
2.8 – Graph Linear Inequalities in Two Variables A linear inequality in two variables can be written in one of these forms: Ax + By < C Ax + By > C An.
Notes Over 2.3 Graphing with the Slope-Intercept Form
Unit 1 – First-Degree Equations and Inequalities
Collins Type 2 (Turned in) Describe when and why you would use the vertical-line test and the horizontal-line test.
Section 1.7 Piecewise Functions. Vocabulary Absolute Value Function – a piecewise function, written as f(x)=, where f(x) 0 for all values of x. Greatest.
2.5 – Rational Functions. Ex. 1 Graph 5 x – 2 Ex. 1 Graph 5 x – 2.
Domains and Graphs of Rational Functions: Lesson 30.
Bell Ringer 1. A bowling alley rents shoes for $1 per hour and lanes for $6 per half hour. Write the equation for the total cost, C, of renting shoes and.
Unit 2 Lesson 2 Remediation 1. The Earnings Section The Deduction Section The Personal Information Section  Parts of a paycheck stub.
4 minutes Warm-Up Graph the function , and then use the horizontal-line test to determine if the inverse is a function.
INTERPRET LINEAR GRAPHS & WRITE LINEAR EQUATIONS SECTION 5.4B.
Lesson 9 – Special Functions Math 2 Honors - Santowski.
2.7 Piecewise Functions p. 114 Up to now, we’ve been looking at functions represented by a single equation. In real life, however, functions are represented.
2-2: Piecewise Functions Unit 2: Linear Functions English Casbarro.
Percents and Equations 6.7. Translations Is = Of = multiplication What = x Turn % into fraction or decimal to compute.
Problems of the Day 1.) Find the slope of the line that contains (–9, 8) and (5, –4). 2.)Find the value of r so that the line through (10, -3) and (r,
5.3.1 Direct Variation. Function A direct variation is a function that can be written as A direct variation is a function that can be written as y=kx.
Writing Equations for Piecewise Functions and Word Problems Chapter 2
Removable Discontinuities & Vertical Asymptotes
Grace enjoys baby-sitting, but it only pays $4 an hour. She has been offered a job as a tutor that pays $8 an hour. She can must work less than 15 hours.
1.6 Step and Piecewise Functions. Objective To identify and graph step and piecewise- defined functions.
Proportions From Tables. Hours WorkedPay You have been hired by your neighbor to babysit their children Friday night. You are paid.
+ Directly Proportional. + Directly proportional: as one amount increases, another amount increases at the same rate. Hence, the straight line when we.
Algebra 2 Monday, 10/6/14 Warm-ups…complete slide below Discussion/Notes/Guided Practice:  Section 2.6: Special Functions Homework: A#2.6 page 99 #14.
Chapter 2 Examples Section 6 Special Functions. Example 1  Psychology  One psychologist charges for counseling at the rate of $85 per hour or any fraction.
Objectives: The student will be able to… 1)Graph exponential functions. 2)Solve exponential equations and inequalities.
2.2 Constant Rates of Change
Warmup 3-24 Simplify. Show work! Solve for x. Show work! 4. 5.
1.7 Piecewise Functions Objective: Identify and graph piecewise functions including greatest integer, step, and absolute value functions.
Rational Functions (Algebraic Fractions)
2.6: Special Functions Algebra 2.
Objective: Review piecewise functions.
Warm Up Graph f(x) = 2x + 3 Graph f(x) = -3x + 1
Piecewise Functions At least 2 equations, each of which applies to a different part of the functions domain. It is like having 3 equations for 3 different.
LESSON 2–6 Special Functions.
Equations with Rational Expressions and Graphs
Piecewise Functions Notes
Rational Functions and Their Graphs
piecewise-defined function
Chapter 7 Jeopardy! Solving Equations
Piecewise Functions.
WEEK 1 FOUNDATION.
OUR GOAL Find: Sec 2.2: Limit of Function and Limit Laws
Greatest Integer Function (Step Function)
Piecewise Functions.
Piecewise Functions At least 2 equations, each of which applies to a different part of the functions domain. It is like having 3 equations for 3 different.
Piecewise-defined Functions
Graphing Step (Greatest Integer) Functions
5 minutes Warm-Up Solve. 1) 2) 3) 4).
Characteristics of Functions
Step Functions Section 3.5.
Warm-Up 4 minutes Graph each function: 1) Y = 3x - 2 Y = -½x + 4 Y = 8
Opening Questions Evaluate the function for the indicated values: f(x) = 3x – 2 1) f(2) 2) f(0) 3) f(-2) Graph the two linear equations on the.
Homework #: TEST tomorrow
Warm-up: Solve each equation for a. 1. 2a–b = 3c
Presentation transcript:

DO NOW – Summarize the steps you would take to solve limits. For example: – When do you factor, expand, plug in, rationalize, etc.? – What is the difference between taking a limit as x approaches a constant and x approaches infinity? – When do you graph the function to solve the limit? – Etc. HOMEWORK – Study for Exam AIM: What do you know about functions and their limits?

Piecewise Functions You have a summer job that pays time and a half for overtime. (If you work more than 40 hours) After that it is 1.5 times your hourly rate of $7.00/hr. 1.Write and graph a piecewise function that gives your weekly pay P in terms of the number hours you work h. 2.How much will you make if you work 45 hours?

Ceiling/Floor Function Musicians receive royalties of 9 cents for songs 5 minutes or less and they receive an additional 1 cent per minute or fraction thereof for songs over 5 minutes. 1.Write an equation to describe the amount of money the musicians make in royalties based on the length of the song. 2.How much money will they earn for a 7.5 minute song?

Find the domain of the function Greatest Integer Function

Asymptotes Find all asymptotes of the function: