Pg. 57/73 Homework Pg. 73# 121 – 128 all Pg. 66 # 1 – 11 odd, 35 – 38 all #61x = 9 ft or 11 ft#62x = 2.50 in #6331, 250 ft 2 #124r = 6.91 units #129Graph#130Q1.

Slides:



Advertisements
Similar presentations
Operations with Functions Objective: Perform operations with functions and find the composition of two functions.
Advertisements

3.7 Optimization Problems
Inverse Functions. Objectives  Students will be able to find inverse functions and verify that two functions are inverse functions of each other.  Students.
Combinations of Functions; Composite Functions
New Functions From Old Functions. 2 Translation: f (x) + k y2y2 Direction of Translation Units Translated Value of k x 2 – 4 x 2 – 2 x x.
 Simplify the following. Section Sum: 2. Difference: 3. Product: 4. Quotient: 5. Composition:
Title of Lesson: Introduction to Functions Section: 1.2Pages:
Lesson 3.1 Objective: SSBAT define and evaluate functions.
We are limited, but we can push back the border of our limitations
Combinations of Functions
Do Now Determine the open intervals over which the following function is increasing, decreasing, or constant. F(x) = | x + 1| + | x – 1| Determine whether.
Accelerated Math II Polynomial Review. Quick Practice “Quiz” 1. A rectangular sheet of metal 36 inches wide is to be made into a trough by turning up.
Section 1-2: Composition of Functions If you have two functions, you can form new functions by adding, subtracting, multiplying, or dividing the functions.
Chapter 7 7.6: Function Operations. Function Operations.
1.6 Operations on Functions and Composition of Functions Pg. 73# 121 – 123, 125 – 128 Pg. 67 # 9 – 17 odd, 39 – 42 all #1212L + 440#122l = 125, A = 125w.
Bellwork Pick up the Domain/Range worksheet and work on the first four (bottom left—pg. 216) with your partner. There is an answer bank on the last sheet.
Operations on Functions Lesson 3.5. Sums and Differences of Functions If f(x) = 3x + 7 and g(x) = x 2 – 5 then, h(x) = f(x) + g(x) = 3x (x 2 – 5)
Warm ups 1. The relation defined by the set of ordered pairs below is not a function. Which pair could be removed to obtain a function?? {(-5,1) (2,3)
OPERATIONS ON FUNCTIONS. Definition. Sum, Difference, Product, Quotient and Composite Functions Let f and g be functions of the variable x. 1. The sum.
Domain/Range/ Function Worksheet Warm Up Functions.
CHAPTER 4 DIFFERENTIATION NHAA/IMK/UNIMAP. INTRODUCTION Differentiation – Process of finding the derivative of a function. Notation NHAA/IMK/UNIMAP.
Ch 9 – Properties and Attributes of Functions 9.4 – Operations with Functions.
Aim: What is the composition of functions? Do Now: Given: Express z in terms of x HW: Work sheet.
Function Composition Given f(x) = 2x + 2 and g(x) = 2, find f ºg(x). f ºg(x)=f(g(x)Start on the inside. f(g(x)) g(x) = 2, so replace it. f(g(x)) = f(2)
 Domain – all of the x-coordinates of a graph  Range – all of the y-coordinates of a graph  Notation ◦ Interval notation ◦ Set Notation  Proper use.
Inverse functions: if f is one-to-one function with domain X and range Y and g is function with domain Y and range X then g is the inverse function of.
3.1 Functions. Determining Inputs and Outputs The cost of a tank of gas depends on the number of gallons purchased. The volume of a cube depends on the.
Homework Questions. QUIZ TIME! Piecewise Day 5  Finding Domain and Range.
Section 2.7 Combining Functions Objectives: To add, subtract, multiply and divide functions. Composition of functions.
Warm-up (10 min. – No Talking) Sketch the graph of each of the following function. State the domain and range. Describe how and to which basic function.
Ch. 7 Day 6 Book Section 7.6 Function Operations.
Combinations of Functions: Composite Functions
3.5 Operations on Functions
Digital Lesson Algebra of Functions.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Quadratic Functions.
Section 2-3b The Product Rule
CHAPTER 4 DIFFERENTIATION.
Prerequisite Skills VOCABULARY CHECK 1
5-Minute Check Lesson 1-2A
Today in Pre-Calculus Notes: (no handout) Go over quiz Homework
1-1 RELATIONS & FUNCTIONS
5.1 Combining Functions Perform arithmetic operations on functions
FUNCTIONS Chapter 1 Section 4.
Objective 1A f(x) = 2x + 3 What is the Range of the function
Warm Up Given y = –x² – x + 2 and the x-value, find the y-value in each… 1. x = –3, y = ____ 2. x = 0, y = ____ 3. x = 1, y = ____ –4 – −3 2 –
3.3 – solving Inequalities (multi-step)
8.2: Graph Simple Rational Functions
Function Composition Section 8-7.
2-6: Combinations of Functions
2.6 Operations on Functions
Combinations of Functions
Composition of Functions
Sec. 2.7 Inverse Functions.
Sullivan Algebra and Trigonometry: Section 3.5
3.5 Operations on Functions
Warm Up Determine the domain of the function.
1.5 Combination of Functions
Functions Collection: notation, inverse, composite
Section 7.2B Domain and Range.
Function Composition Section 8-7.
Composition of Functions
Function Composition.
2.1 Functions.
Combinations of Functions
2-6: Combinations of Functions
f(x) g(x) x x (-8,5) (8,4) (8,3) (3,0) (-4,-1) (-7,-1) (3,-2) (0,-3)
Function Composition R. Yates.
FUNCTIONS & THEIR GRAPHS
Presentation transcript:

Pg. 57/73 Homework Pg. 73# 121 – 128 all Pg. 66 # 1 – 11 odd, 35 – 38 all #61x = 9 ft or 11 ft#62x = 2.50 in #6331, 250 ft 2 #124r = 6.91 units #129Graph#130Q1 integers #131(800, )#143s(t) = -16t 2 +70t+200 #144Graph#145Q1 #146t = 0.39, 3.98 sec#147(0.39, 3.98)

Pg. 73 Homework Problems #124 A = π r = π r 2 solve for r and you get r ≈ # s(t) = -16t t = -16t t t = and t = When t is between those values.

1.6 Operations on Functions and Composition of Functions A long rectangular sheet of metal 10 in. wide is to be made into a gutter by turning up sides of equal length perpendicular to the sheet. Find the length that must be turned up to produce a gutter with maximum cross- sectional area.

1.6 Operations on Functions and Composition of Functions Operations of FunctionsDomain and Range The domain of the new function created consists of all numbers x that belong to the domains of both f and g. The quotients domain also requires that g(x) ≠ 0.

1.6 Operations on Functions and Composition of Functions Practice Let and Find State the domain for each. Now for and try:

1.6 Operations on Functions and Composition of Functions Composition of Functions Notation is given by: In order for a value of x to be in the domain of f◦g, two conditions must be met: – x must be in the domain of f – f(x) must be in the domain of g Practice Let and – Find and and determine their domain. Let and – Find and and determine their domain.