The Twelve Basic Functions Section 1.3 Pgs 102 – 103 are very important!

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Presentation transcript:

The Twelve Basic Functions Section 1.3 Pgs 102 – 103 are very important!

After today’s lesson you will be able to: Recognize graphs of twelve basic functions and describe their characteristics Determine domains of functions related to the twelve basic functions Combine the twelve basic functions in various ways to create new functions

Looking for Domains Nine of the functions have domain the set of all real numbers. Which 3 do not? One of the functions has domain the set of all reals except 0. Which function is it, and why is 0 not in the domain? Which of the two functions have no negative numbers in their domains? Of these two, which one is defined at 0?

Looking for continuity Only two of the twelve function have points of discontinuity. Which functions are they? Are these points in the domain of the function?

Looking for boundedness Only three of the twelve basic functions are bounded. Which 3?

Looking for symmetry Three of the twelve basic functions are even. Which are they?

Ex1 Which of the basic functions are continuous? For the functions that are discontinuous, identify as infinite or jump. ContinuousJump Discontinuity Infinite Discontinuity

Ex 2 Which of the basic functions have symmetry? Describe each. Symmetry in x-axis Symmetry in y-axis (even) Symmetry in origin (odd)

Exploration: Looking for Asymptotes 1)Two of the basic functions have vertical asymptotes at x = 0. Which two? 2)Form a new function by adding these functions together. Does the new function have a vertical asymptote at x = 0? 3)Three of the basic functions have horizontal asymptotes at y = 0. Which three? 4)Form a new function by adding these functions together. Does the new function have a horizontal asymptote y = 0? 5)Graph f(x) = 1/x, g(x) = 1/(2x 2 -x), and h(x) = f(x) + g(x). Does h(x) have a vertical asymptote at x = 0? Explain.

Piecewise-defined Functions Which of the twelve basic functions has the following piecewise definition over separate intervals of its domain? xif x  0 f(x) = -xif x < 0

Ex 3 Use the basic functions from this lesson to construct a piecewise definition for the function shown. Is your function continuous?

Ex4 To what basic functions does w(x) = x 3 – 2x 2 + x relate? Describe the behavior of the function above.