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Understanding Functions and Graphs in Pre-Calculus

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This lesson explores the fundamental concepts of functions and their graphs in pre-calculus. Students will graph lines and piecewise functions, define essential terms such as function, domain, and range, and perform the vertical line test. They will also learn to use function notation, calculate rates of change, and identify basic graphs. Various online resources, including interactive tutorials and assignments, will support their understanding of functions, including translations and compositions. Homework will reinforce concepts covered in class.

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Understanding Functions and Graphs in Pre-Calculus

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  1. Pre-CalcUnit 2 FUNCTIONS & Graphs http://math-b.hyde.wikispaces.net/ http://rechneronline.de/function-graphs/ http://graph.seriesmathstudy.com/

  2. Do Now • Graph the line that goes thru (2.5, 4) and (3.7, 5) • In Class • define “Function,” “Domain,” and “Range” • Demonstrate the vertical line test • Use function notation • Show 3 example of Rate of Change formula • pp: 114 - 117 • #s: 9, 15, 23, 35, 99 • HOMEWORK: • pp: 114 - 117 • #s: 10, 16, 24, 36, 48, 58, 68, 71, 90, 100 http://www.analyzemath.com/DomainRange/DomainRange.html Finding DOMAIN - RANGE • Pre-Calc TUTORIALS Good Web pages • http://www.analyzemath.com/PrecalculusTutorials.html • http://www.analyzemath.com/DomainRange/domain_range_functions.html Unit 2 Lesson one: 2.1 Functions

  3. Do Now: • Find the Domain and Range of f(x) = 1 / (x – 2) • In Class • Go to page xix and xx and interpret SIX basic function graphs • Describe 3 types of piecewise functions • Demonstrate the understand of the concepts of “Increasing,” “Decreasing,” and “Constant” • HOMEWORK: • pp: 114-117 • #s: 32, 42, 54, 66, 72, 78, 82, 86, 91 • Identify Basic Graphs and match to their equation • http://www.analyzemath.com/Graph1/GraphFunctionsTutorials.html Unit 2 Lesson two: More Functions: 2.1

  4. Do Now: Graph the piece wise function: • [-10, 0] f(x) = 3x+2 • [2, ∞] f(x) = x2 +4 • In Classlook on page xix and xx • Graph Square and Square Root functions • Graph Cube and Cube Root functions • Graph Parabola and Semi Circle • Graph special “Weird” functions Piecewise and Greatest Integer • pp: 126 -127 • #s:15 – 25 ODD • 31 – 41 ODD • HOMEWORK: • pp: 126 -127 • #s:15 – 25 ALL • 33 – 37 ALL • 47 – 53 ODD Graphs of Functions and Algebra - Interactive Tutorials http://www.analyzemath.com/precalculus.html Unit 2 Lesson three: Oct 5Graphs of Functions 2.2

  5. Do Now: • pg 126 For Thought 1-9 ODD • In Class: • Pp:128 – 129 • 63,65,67,69 • HOMEWORK: • Pp:128 – 129 • 63,65,67,69, 81 – 84 ALL • (H) 73-77 ODD, 85 • Graph Square and Square Root functions • Graph Cube and Cube Root functions • Graph Parabola and Semi Circle • Graph special “Weird” functions Piecewise and Greatest Integer • Pg xix & xx • Page: 179 - 180 Unit 2 Lesson four: more graphs Oct 4 Graphs of Functions and Algebra - Interactive Tutorials http://www.analyzemath.com/precalculus.html

  6. Do Now: • Page 128 #67 • In Class: • pp: 142-143 • #s: 5, 17, 25, 31, 35, 45 • HOMEWORK: • pp: 142-143 • #s: 5,7, 17, 18 25, 28, 31, 35, 37, 45 • (H) 19-24 ALL Unit 2 Lesson 5: Translations of Graphs OCT 11 • TRANSLATIONS of FUNCTIONS • http://rechneronline.de/function-graphs/ • INVERSE FUNCTIONS • http://www.analyzemath.com/inversefunction/Tutorials.html

  7. Do Now: • Graph • f(x) = (x^3) • f(x) = x^{1/3} • In Class: • pp: 144-145 • #s: 71-79 ODD • HOMEWORK: • pp: 144-145 • #s: 71-79 all, 93,95, • (H) 96, 97 Unit 2 Lesson six: Translations of Graphs OCT 13 • TRANSLATIONS of FUNCTIONS • http://rechneronline.de/function-graphs/ • INVERSE FUNCTIONS • http://www.analyzemath.com/inversefunction/Tutorials.html

  8. Do Now: • Graph: • f(x) = x2 • f(x) = x2+ 2 • f(x) = (x-3)2 • In Class: • page 147 &149 definitions • Define • “Sum Functions,” • “Difference Functions,” • “Product Functions,” and “Quotient Functions” • Composition of functions • HOMEWORK: • pp:153 • #s: 1, 5, 17, 21, 29, 35, 49, 61 71, 79 • #7a:pp169 - 170 • 87, 91,93, Unit 2 Lesson 7: Operations with Functions 2.4 Oct 14 Compositions of functions f(x) and g(x)  f ° g(x) = f([g(x)] http://www.analyzemath.com/CompositionFunction/CompositionTest.html

  9. Do Now • Page 153 #29 • In Class: • define “Variation” and “Proportionality” • direct variation pp 172 -173 • inverse variation • joint variation • combined variation • HOMEWORK: • pp: 176 - 177 • #s: 3, 11, 17, 19, 23, 27, 33, 37, 41, 43 • http://www.analyzemath.com/Graph-Basic-Functions/Graph-Basic-Functions.html • http://www.analyzemath.com/precalculus.html Unit 2 Lesson Eight: Oct 172.6 Constructing Functions with Variation

  10. Do Now • In Class • HOMEWORK: Unit 2 Lesson one

  11. Do Now • In Class • HOMEWORK: Unit 2 Lesson one

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