Chapter 1

Mathematical Model  A mathematical model is a graphical, verbal, numerical, or symbolic representation of a problem situation.

Example- Page Teacher Salary Comparison Over 60% of men not in the teaching profession earn a higher salary than men who are teachers. The table shows how much more money the average college-educated male non-teacher makes as compared to the average male teacher. YearPercent More Earned by Non- Teachers as Compared to Teachers % % % % % % % Source: For example, in 1990 male non-teachers made 37.5% more than male teachers on average.

Example- Page 17 a. Describe the trend observed in these data. b. Why was there such a big jump in the percentage of non-teachers who earn a higher salary than teachers from 1990 to 2000? c. What does the –3.6% in 1940 indicate about salaries of male teachers?

Example- Page Super Bowl Ticket Prices The table shows the price of a Super Bowl ticket for selected Super Bowls. Super Bowl TicketFace Value I (1)$10 V (5)$15 X (10)$20 XV (15)$40 XX (20)$75 XXV (25)$150 XXX (30)$300 XXXV (35)$325 XL (40)$600 (Source:

a. Describe the trend seen in these data. Are prices increasing or decreasing over time? b. Compare the difference in ticket face value from one year to the next. What patterns do you notice? c. Predict the face value of a ticket for the 60 th Super Bowl.

1.2

Function Notation  y = f(x)  Input (independent variable)  Output (dependent variable)

Functions  A relation is a function if each input value has exactly one output value

Determining Functions  Determine if the relation is a function  (3, 2), (4, 2), (5, 2)  (1, 2), (-1, 3), (1, 7)

Vertical Line Test  Use the vertical line test to determine whether each graph represents a function

Evaluating Functions

1.3

Constant Functions  A constant function is represented by f(x) = b, where b is a fixed number  When graphed, these are horizontal lines

Linear Functions  A linear function is represented by f(x) = mx + b, where b is a fixed number  m is the slope  b is the y-intercept  Linear Functions have a constant rate of change (the slope)

Slope  Slope = rate of change or= change in y change in x = ∆y or ∆x or= Rise Run

Slope- given points  For points, slope =  A positive slope goes up as you read the graph from left to right. (A negative slope goes down as you read the graph from left to right.)  As the absolute value of the slope gets larger, the steepness of the incline increases.

Examples  Calculate the slope between each pair of points  (7, 2) and (4, -3)  (8, 2) and (-8, 6)

Nonlinear Functions  If the rate of change is not constant, it is not a linear function

1.4

Two-Variable Data  Ordered Pair  Relation  Domain  Range

 State the Domain and the Range  (2, 3), (-3, 7), (8,3)