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basic functions
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12 basic functions Parent functions (the most basic way to write this function) Identity function: f(x) = x Squaring function: f(x) = x2 The cubing function: f(x) = x3 The reciprocal function: f(x) = 1/x The square root function: f(x) = The exponential function: f(x) = ex The Natural logarithm function: f(x) = ln x
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8) The sine function: f(x) = sin x 9) The cosine function: f(x) = cos x 10) The absolute value function: f(x) = |x| 11) The greatest integer function: f(x) = int (x) 12) The logistic function: f(x) = e-x
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Questions Look at the handout of the 12 basic functions for the following questions. 1) 9 of the functions have domain (-∞,∞). Which 3 do not? 2) 1 of the functions has the domain of (-∞, 0) U (0, ∞). Which function is it, and why is it 0? 3) which 2 functions have no negative numbers in their domain? Of these 2, which one is defined at 0?
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4) Only 2 of 12 functions have points of discontinuity
4) Only 2 of 12 functions have points of discontinuity. Which 2 are they? Are these points in the domain? 5) Only 3 of 12 basic functions are bounded. Which 3? 6) 3 of 12 functions are even. Which are they?
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Group activity In groups of 4 or less: do exploration 1 on p. 104
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Piecewise Functions Piecewise functions are functions that have conditions on them For example:
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examples Graph the piecewise function: 1) 2)
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Homework p #1-34 all, 45, 48, 51
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