Chapter 1 functions

1.1
Functions and Their Graphs

Piecewise-Defined Functions
Sometimes a function is described in pieces by using different formulas on different parts
of its domain.

Linear Functions A function of the form ƒ(x) = mx + b, where m and b are fixed constants, is called a linear function. Figure 1.14a shows an array of lines ƒ(x) = mx. Each of these has b = 0, so these lines pass through the origin. The function ƒ(x) = x where m = 1 and b = 0 is called the identity function. Constant functions result when the slope is m = 0

Algebraic Functions Any function constructed from polynomials using algebraic operations (addition, subtraction, multiplication, division, and taking roots) lies within the class of algebraic functions.
Trigonometric Functions
Logarithmic Functions
Transcendental Functions

1.2
Combining Functions;
Shifting and Scaling Graphs

1.3
Trigonometric Functions

1.4
Graphing with
Calculators and Computers