The document discusses functions and how to determine if a relationship represents a function using the vertical line test. It defines what constitutes a function and introduces function notation. Examples are provided of evaluating functions for given values of the independent variable and using functions to model and express relationships between variables.

1. Functions Students will determine if a given equation is a function using the vertical line test and evaluate functions given member(s) of the domain.

2. | -2 Interval Notation Algebraic Notation Graph Interval Notation x > 3 -1 ≤ x < 5 x < -2 or x ≥ 4 | 3 o | -1 | 5  o | 4 o 

3. A function is a relationship or correspondence between two sets of numbers, in which each member of the first set (called the domain ) corresponds to one an only one member of the second set (called the range ). Function, Domain, and Range

4. Domain Range X Y f x 2 x 1 x 3 y 2 y 1 y 3 Mapping

5. Functions? State the domain and range. Function Domain: {-2, 3, 5} Range: {1, -2, 7} Function Domain: {-4, 1, 6} Range: {1, -8} Not A Function

6. Determine which of the following relations represent functions. Not a function Function Function

7. Vertical-Line Test If every vertical line intersects a given graph at no more than one point, then the graph represents a function. function not a function

8. x y Not a function. Function?

9. x y Function.

10. Function Notation f (x) f is the name of the function x is the variable into which we substitute values or other expressions x is called the independent variable and f ( x ) is the dependent variable . Does Not Mean f times x. Read: “f of x”

11. Evaluating Functions Let f ( x )=2 x – 3 and g ( m ) = m 2 – 2 m + 1. Determine: a.) f (-3) c.) f ( 1/2 ) b.) g (-2) d.) g ( a + 1)

12. Modeling With Functions Example 1 Express the surface area of a cube as a function of its volume. Example 2 A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 30 ft, express the area A of the window as a function of the width x of the window.