1.3 12 basic functions

1. 1.3 12 basic functions

2. 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

3. 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) = 1 1 + e-x

4. 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?

5. 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?

6. Group activity • In groups of 4 or less: do exploration 1 on p. 104

7. Piecewise Functions • Piecewise functions are functions that have conditions on them • For example:

8. examples • Graph the piecewise function: • 1) • 2)

9. Homework • p. 106-107 #1-34 all, 45, 48, 51