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

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

The Twelve Basic Functions the 12 functions are found on page 102-103 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)

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

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

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

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

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)

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: