Two Main Classes of Elementary Functions (1/26/09) Algebraic functions. These are functions in which the output comes starting with the input variable and doing nothing but combinations of powers, sums, differences, products and quotients. Transcendental functions. These are function which are not algebraic.

Types of Algebraic Functions Linear functions Polynomial functions Power functions Rational functions Combinations of the above

Clicker Question 1 The function f (x) = 3x +  x is a A. linear function B. polynomial function C. power function D. rational function

Types of Transcendental Functions Trigonometric (“circular”, “periodic”) functions Exponential functions Logarithmic functions Others, including hyperbolic

Clicker Question 2 The function g (x)= x x is a A. polynomial function B. power function C. rational function D. transcendental function

Mathematical Models Again When applied mathematicians try to model natural phenomena with functions, they must pick the most appropriate types of elementary functions. If possible, linear models are great (easy to work with), but they often don’t describe the situation accurately.

Examples Distance traveled by a car driving at a constant rate. Height of a ball thrown upwards. Amount of daylight each day over a year in Saratoga Springs. Number of bacteria in a new culture. Intensity of an earthquake.

Clicker Question 3 What type of function would best model the amount of money in an account which earns 8% interest compounded monthly? A. polynomial function B. power function C. trig function D. exponential function E. log function

Clicker Question 4 What type of function would best model the y – coordinate on a “unit circle” (i.e., a circle of radius 1) as you move around the circle counterclockwise starting at (1, 0)? A. polynomial function B. power function C. trig function D. exponential function E. log function

Assignment for Wednesday Read Section 1.2 Do Sec 1.2 Exercises 1, 3, 5, 7, 9, 13, 15, 17, 19, 20, 21 a and b.