Overview
Objectives
Identify the identity, squaring, cubic, and absolute value functions and graph them
Identify and graph piecewise-defined functions
Use graphing techniques such as stretching, shrinking, reflecting, and translation to graph a function
Become familiar with the concept of symmetry and the concept of even and odd functions
Instructions
Discussion questions are important interactive learning and sharing activities in this online course. You will stay involved, ask questions, and learn from each other. Your instructor will monitor the content quality-depth and breadth both, makes suggestions and moderate the discussion session. No late Discussions or participation postings are allowed. Day 4 (Thursday) of the week is the discussion closing day. Discussion counts 3-points.
All students must respond discussion question on MONDAY of the week by making a response posted. This will count as one (1) posting.
Post two (2) or more additional participation response postings substantiated by algebraic examples, related applications, and research. You need to click “reply” after you are inside your classmates’ DQ posting.
Make sure you review: https://www.purplemath.com/modules/fcntrans.htm
Discussion Question(s) : Respond to all steps in one DQ response posting thread
Post a response to the following questions in three steps on the discussion board
Step 1: What one area from the readings on Chapter 1 Functions is you most comfortable with? Why do you think that is? Using what you know about this area, create a discussion question that would trigger a discussion. Demonstrate your ideas with algebraic examples.
Step 2: Write your response to the following items from a) to e)
a) From this week’s reading, identify and describe how the piecewise-defined functions are different from other basic functions, and quote your reading with page number, website URL, or any other source where classmates can go for a review.
b) Now, let [Image unavailable: h left parenthesis x right parenthesis space equals space open curly brackets table attributes columnalign left end attributes row cell vertical line x vertical line space space space space space space x less than space 0 end cell row cell x squared space space space space space space space space x space greater or equal than 0 end cell end table close parentheses]
Find: i) h(0) =
ii) h(-2) =
iii) h(3) =
c) What is the domain of the functions:
[Image unavailable: i right parenthesis space space f left parenthesis x right parenthesis space equals space x squared comma space space space space i i right parenthesis space space f left parenthesis x right parenthesis space space equals fraction numerator 3 over denominator x minus 1 end fraction comma space space i i i right parenthesis space f left parenthesis x right parenthesis space equals square root of x plus 1 end root]
d) Let [Image unavailable: f left parenthesis x right parenthesis space equals space x squared], which one of these is stretching or shrinking: