Functions and Their Graphs Chapter 1 Pre-calculus Honors

Transcription

1 Functions and Their Graphs Chapter 1 Pre-calculus Honors Just as ripples spread out when a single pebble is dropped into water, the actions of individuals can have far reaching effects. -Dalai Lama Page1

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3 Pre-Calculus Honors 2016/2017 Chapter 1 Functions and Graphs Assignment Sheet HONORS Note: Gray box problems in your text book are Non-Calculator Problems. There may be others as well! Day Functions and Their Properties p.94 95: #1-17 odds Day Functions and Their Properties p.95 96: #25, 28, 31,34-37, 43, 45, 73, 75 Day Functions and Their Properties p No Calculator on all: # 6-14 evens, 33, odds Day Twelve Basic Functions Complete the remaining charts in your packet for this section Day Twelve Basic Functions p.106 #: 1-28, 35, 39 Day Twelve Basic Functions p.107 #: 45-47, 51, Day Building Functions from Functions p.116 #: 1-7 odds, 11, 13 Day Building Functions from Functions p.117 #: 12, 14, 15, 17, 19, 21, 33, Day Building Functions from Functions Application Continued Page3

4 Day Parametric Relations and Inverses p : # 9-12, 13, 15, 17, Day Parametric Relations and Inverses p : # 21, 27, 29, 31, 33, 41,43 Day Graphical Transformations p : # 5, 9, 12, 13, 14, 17,19, Day Graphical Transformations p : # 25, 27, 33, 39 (a) only, 40 (a) only, 43, 44, 47,49, Day 14 Review p : #1 10 all, all (find domain without calculator, but you may use your calculator for the range exept for #18), 19 and 20 (continuity only), 26 and (all on calculator), 34, (algebraically only- no calculator except for 38,40) p : #42, all, all NON-Calculator, 59 By the end of this unit you should be able to. 1. Evaluate functions and find their domain and range without a calculator 2. Recognize functions (graphically and algebraically) and be able to distringuish them from relations 3. Evaluate and graph piecewise functions 4. Analyze and sketch the graphs of parent functions, determine continuity, boundedness, local and absolute extrema, even/odd, increasing/decreasing 5. Graph transformations of functions 6. Find arithmetic combinations and compositions of functions numerically, algebraically, and graphically and determine the domain 7. Find inverses of functions graphically and algebraically and verify with function composition Page4

5 1.2 Functions and Their Properties When is a relation a function? A function from a set D to set R is that assigns every element in D (called ) to exactly one element in R (called ). Euler s function notation y = f(x), where x is the variable and y is the variable. Is it a function? Birthday rule: Instrument rule: Social Security rule: Are any of these one-to-one functions? Can you come up with other one-to-one functions in the real world? Are the following functions? 1. f(x) = x 2 2. x 2 + y = 1 3. g(x) = 5x y = x 1/3 5. y 2 + x = 1 6. y 2 = x x = y + 2 Page5

6 What makes a function a function? Describe verbally Show numerically Algebraically Graphically Important Vocabulary for section 1.2 Domain, Range, dependent variable, independent variable, continuity, increasing, decreasing, boundedness, local and absolute extrema, end behavior What is the domain of a function? Definition: In your own words: Finding the Domain of a function without using the calculator. Let s try determining the domain of the following functions. Consider each problem 3 ways: Algebraically, Graphically Numerically. 1. h(x) = x f(x) = 5x 4 x 3. h(x) = 4 3x Page6

7 4. m(x) = 11 2x x 2 5. g(x) = 5 2x r(x) = x 8 7. f(x) = log 2 x 8. m(x) = 4 x 9. r(x) = x f(x) = 9 x f(x) = x 2 9 Things to look for when finding the domain of a function algebraically: Page7

8 Ways to describe the graph of a function Increasing (p.87) Decreasing (p.87) End Behavior Continuity (p.84) Boundedness (p.88 89) Local and absolute extrema Page8

9 Referring to the graph, classify the function as a. bounded above only b. bounded below only c. bounded d. not bounded Referring to the graph, classify the function as a. bounded above only b. bounded below only c. bounded d. not bounded Referring to the graph, classify the function as a. bounded above only b. bounded below only c. bounded d. not bounded Referring to the graph, classify the function as a. bounded above only b. bounded below only c. bounded d. not bounded Page9

10 In the following graph, determine if/where the function is Continuous? Bounded? Increasing? Decreasing? Label all local/absolute extrema? What would you change to make the graph discontinuous? In the following graph, determine if/where the function is Continuous? Bounded? Increasing? Decreasing? Label all local/absolute extrema? Page10