1.3 12 basic functions

12 basic functions

Parent functions (the most basic way to write this function)

1) Identity function: f(x) = x2) Squaring function: f(x) = x2

3) The cubing function: f(x) = x3

4) The reciprocal function: f(x) = 1/x5) The square root function: f(x) =6) The exponential function: f(x) = ex

7) The Natural logarithm function: f(x) = ln x

8) The sine function: f(x) = sin x9) The cosine function: f(x) = cos x10) 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

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?

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?

Group activity

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

Piecewise Functions

• Piecewise functions are functions that have conditions on them

• For example:

examples

• Graph the piecewise function:• 1)

• 2)

Homework

• p. 106-107 #1-34 all, 45, 48, 51