1. The Twelve Basic Functions
Section 1-3
The Twelve Basic Functions

2. Section 1-3 the twelve basic functions
studying their domain, continuity, boundedness, and symmetry
analyzing functions graphically
piecewise functions

3. The Twelve Basic Functions
the 12 functions are found on page
study them carefully so you know the characteristics of each function
some of these functions you have already studied and know well (identity, squaring, cubing, absolute value)
some of these functions you have already studied but we will cover them again (reciprocal, square root, exponential, log., sine, cosine)
some of these functions are new and will be also covered this year (greatest int. and logistic)

4. Domain
Question: Nine of the functions have a domain of all reals, which three do not?
Answer: square root, natural log., and reciprocal

5. Continuity Question: Which two functions have points of discontinuity?
Answer: reciprocal and greatest integer

6. Boundedness
Question: Which of the three functions are bounded (above and below)?
Answer: sine, cosine, and logistic

7. Symmetry Question: Which of the functions are even?
Answer: squaring, cosine, absolute value

8. Analyzing Functions Graphically
some functions we study will be an alteration of one of the basic 12
if we are asked to analyze such a function we will need to graph it (by hand or with the graphing calculator)
look at each characteristic of functions that we studied in the last section in respect to the graph (domain, range, symmetry, local extrema, incr/decr, continuity, boundedness, asymptotes, and end behavior)

9. Piecewise-Defined Functions
these are functions that come in parts, having a different equation for different values of the domain
many piecewise functions have jump discontinuities
here is an example: