Section 1.2 - Functions and Their Properties

Essential Question(s): 

What are general properties of functions?

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Follow these four steps to complete this "flip" lesson.

STEP 1: Title your spiral with the heading above and copy the essential question(s).

STEP 2: Copy and define the following groups of vocabulary using your textbook glossary. This can be any tables, properties, theorems, terms, phrases or postulates listed. The vocabulary is grouped with specific examples.

Group 1 Vocab

• definition box pg 86 (function, domain, range)
• pg 86 What is function notation? (include independent and dependent variable)
• pg 88 What is implied and relevant domain? (agreement box)
• What is the Vertical Line Test? pg 87

Group 2 Vocab

• What are the types of continuity for functions? pg 91 (include graphs and any text you feel necessary)
• What does it mean for a function to be continuous or discontinuous? (bottom paragraph of pg 91; copy as needed)

Group 3 Vocab

• How do you know if a function is increasing, decreasing, or constant? (definition box pg 93)

Group 4 Vocab

• What is boundedness? (first the definition box on pg 95, then four pictures above the definition box)
• Can a function be bounded on an interval? (pg 95 below definition box)
• What is local and absolute extrema? (definition box pg 96)
• What are some tips for using a grapher to find local extrema? (bottom left of pg 96; read and copy as needed)

Group 5 Vocab

• What does symmetry with respect to the y-axis look like? (Example: f(x) = x^2 pg 97)
• What does symmetry with respect to the x-axis look like? (Example: x = y^2 pg 97)
• What does symmetry with respect to the origin look like? (Example: f(x) = x^3)
• How can asymptotes be stated? (bottom paragraph pg 99)
• What is the definition of horizontal and vertical asymptotes? (definition box pg 100)
• What are some tips on zooming when looking at end behavior? (pg 101 upper-left)

STEP 3: Read the following page and take any extra notes as needed. Copy the following example(s) from the textbook AFTER their designated Vocabulary Group.

Group 1 Example(s)

• How do you find the domain of a function algebraically? EX 3 pg 88; take notes as needed;

Group 3 Example(s)

• How do you analyze a function's increasing or decreasing behavior? EX 6 pg 94; take notes as needed;

• Read pages 86-101 and then move onto step 4