Clicker Question 1 Are you (and your clicker) here? A. Yes B. No C. Not sure. Too early.

Key Concept: Function (1/23/09) A function is a rule which assigns to every element of an input set (the domain) a single element of an output set (the range). You can think of a function as a machine, taking in an input value and putting out an output value. Or think of it as arrows pointing from the domain to the range.

4 Ways to Represent a Function Verbally : Describe it in words. Example? Numerically : Make a table of values. Example? Visually : Draw a graph. Example? Algebraically : Find a formula. Example?

Some Ideas about Functions If not otherwise stated, the domain of a function in calculus is all real numbers which can be put into the function. Examples Vertical Line Test for the graphs: A graph in the plane is a function of the horizontal variable if and only if each vertical line intersects the graph at most once. Examples

Clicker Question 2 What is the domain of the function f (x) = 1 /  (2x +4)? A. All reals B. All x > 2 C. All x > 0 D. All x > -2 E. All x  -2

Clicker Question 3 Is x 2 + y 2 = 9 a function? A. Yes, because it passes the Vertical Line Test. B. No, because it does not pass the Vertical Line Test. C. y is a function of x, but x is not a function of y.

Piecewise-Defined Functions Functions defined by formula may be defined by different formulas on different parts of the domain. Examples A prime example is the absolute value function |x |.

Clicker Question 4 The function f (x) = |x – 4| can be “piecewise described” by: A. x – 4 if x  - 4; x + 4 if x < - 4 B. x – 4 if x < 4; x + 4 if x  4 C. x – 4 if x  4; -x + 4 if x < 4 D. x if x  4; -x if x < 4 E. You can search me

Mathematical Modeling This means to try to capture realities of some physical situation in terms of functions. Often a labeled picture can be helpful. Example: A rectangle has an area of 40 square inches. Express the perimeter of the rectangle as a function of the length of one of its sides.

Clicker Question 5 Express the area A of a circle as a function of its diameter d. A. A =  d B. A = ¼  d 2 C. A = ½  d 2 D. A =  d 2 E. A = ½  d

Assignment for Monday Read Section 1.1 Do Sec 1.1 Exercises 1, 5-8, 11, 12, 19, 27, 29, 37, 39, 43, 45, 49, 51, 53, 57.