The course covers the main topics of functions in pre-calculus, including characteristics of functions, implied domain, transformations of functions, piecewise functions, operations of functions, and inverse of functions.
Students will learn how to write informal and mathematical descriptions of graphs, determine domains, graph inequalities, identify discontinuities, evaluate functions, describe transformations, graph piecewise functions, perform operations on functions, find inverses, and determine domains and ranges.
The teaching method involves detailed explanations with multiple examples to help students build a solid foundation in pre-calculus functions.
This course is intended for individuals studying pre-calculus or anyone interested in gaining a comprehensive understanding of functions in pre-calculus.
Overview
Syllabus
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Example 01: Write Informal Description of Given Graphs .
Example 02: Write mathematical descriptions given graphs .
Implied Domain .
Warm-up: Evaluating Functions .
Example 01: Determine the domain of the following functions .
Example 02: Graph Inequalities on a number line .
Example 03: Graph the Domain of the Functions .
Example 04: Determine the Domain of the Radical Functions .
Example 05: Determine the Domain of the Rational Functions .
Example 06: Determine the Domain of the Rational/Radical Functions .
Example 07: Identify the Type of Discontinuity as a Hole or Asymptote .
Transformations of Functions .
Warm up: Evaluate the Point of the Functions & Then Graph the Coordinate Points .
Example 01: Describe the Graph of the Transformation of a Function & Find Domain and Range of the Transform Function .
Example 02: Describe the Transformation of Function as well as Determine Domain & Range .
Example 03: Find the Transformation of Function as well as Determine Domain & Range .
Example 04: Describe the Transformation of the Following Functions .
Example 05: Describe the Transformation that are Required to Transform f(x) to g(x) .
Example 06: Given the Transformation, Write the Equations of the Functions .
Piecewise Functions .
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Example 02: Graph the Equations & Determine the Domain Based on the Restrictions .
Example 03: Graph the Functions with Domain Restrictions on the Same Graph & Then Determine the Domain, Range and Type of Discontinuity .
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Operations of Functions .
Example 01: Evaluate the Following Function for the Given Value .
Example 02: Add or Subtract the Functions,Simplify, Determine the Domain & Evaluate for x=-1 .
Example 03: Multiply or Divide the Functions,Simplify, Determine the Domain & Evaluate for x=0 .
Example 04: Find the Compose Functions,Determine the Domain & Evaluate for x=1 .
Example 05: Determine the Functions are Even Odd or Neither .
Inverse of the Functions .
Example 01: Solving Equation for x .
Example 02: Find Inverse, Domain & Range of the Functions .
Example 03: Determine the Inverse of the Functions with Restrictions .
Example 04: Find Inverse, Domain & Range of the Functions .
Taught by
Brian McLogan
