Functions and Graphs

F.1 - Functions, Domain, Range

Objectives

• • Define and Recognize Functions

  • Determine the domain and range of a function

  • Recognize even and odd functions

Activities

• 1. Video F1A - Functions, Domain, Range- In this video I define functions and cover interval and set builder notation for specifying domain and range.

  2. Video F1B - Graphing Functions, Zeros, Asymptotes, and Symmetry - A review of intercepts and sketching graphs

  3. Video F1C - Combining Functions - Addition, multiplication, and composition of Functions

  4. Reading 1.1 from openstax Calculus vol. 1

     1. Do the Checkpoint Problems 

     2. Practice Problems 1.1: 7, 10, 12-14, 17, 20, 28, 30, 31, 36, 39, 41, 42, 44, 47, 50, 52, 56 

F.2 - Classes of Functions

Objectives

• • Write slope intercept and point slope form of a line

  • Recognize degree of a polynomial

  • Find the roots of a quadratic

  • Describe and graph basic functions

  • Review translations/transformations

Activities

• Video F2A - Lines

• Video F2B - Polynomials

• Video F2C - Transformations

• Reading 1.2 from Openstax Calculus Vol. 1

  • Checkpoint Problems

  • Practice Problems: 59, 62, 65, 66, 68, 71, 73, 75, 77, 82, 84, 87, 89, 105

F.3 - Trig Review

Objectives

• • Describe radian measure and relate it to degrees

  • Define 6 trig functions in terms of circles or right triangles

  • Use 30-60-90 and 45-45-90 and quadrants to determine value of trig functions at major points

  • Graph the trig functions

Activities

• Video F3A - Radians and the Unit Circle

• Video F3B - Triangles, Unit Circle

• Video F3C - Graphing trig functions

• Reading 1.3 

• Practice Problems 113, 115, 120, 121, 123-128, 130, 133, 155-158, 163, 165

F.4 - Exponential, Logarithmic and Inverse functions

Objectives

• • Explain when a function has an inverse and 1-to-1 means (Hz Line Test)

  • Find the inverse of a function (if possible)

  • Graph an inverse function

  • Describe logarithmic and exponential functions and relate them

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Activities

• Reading 1.4 and 1.5, can ignore section on hyperbolic functions

• Practice problems: 183-194, 199, 201, 204, 216, 218

• Practice Problems: 229, 231, 233-238, 246-263, 270-277, 279, 282, 284-293, 307

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