Concepts of Relations and Functions and How They are Represented Functions are used by mathematicians and scientists to describe relationships between variable quantities Play a central role in calculus and its applications Use paired data

Study Hours Regents Score Tables and Scatter Plot

Old Faithful Eruptions Scatter Plot

Line graph – join the successive points

Histogram/Bar Graph

Functions Tables, graphs, and equations: Provide three methods for describing how one property depends on another Tables - numericalGraphs - visual Equations - algebraic

A relation is a function if: for each x there is one and only one y. A relation is a one-to-one if also: for each y there is one and only one x. In other words, a function is one-to-one on domain D if: whenever

To be one-to-one, a function must pass the horizontal line test as well as the vertical line test. one-to-onenot one-to-onenot a function (also not one-to-one)

If a variable y depends on a variable x in such a way that each value of x determines exactly one value of y, then we say that y is a function of x. A function f is a rule that associates a unique output with each input. If the input is denoted by x, then the output is denoted by f(x) (read “f of x”). Functions are represented four basic ways: 1) Numerically by tables 2) Geometrically by graphs 3) Algebraically by formulas 4) Verbally

Curve fitting Converting numerical representations of functions into algebraic formulas

Discrete vs Continuous Data Discrete Data: Data that makes discrete jumps. Data represented by scatter plots consisting of isolated points. Data that has a finite number of values and there is space on a number line between 2 possible values. Usually whole numbers. Continuous Data: Data that has values that vary continuously over an interval. Data that is continuous and unbroken curves. Usually a physical measurement, can increase/decrease in minutely small values.

Classify each set of data as discrete or continuous. 1) The number of suitcases lost by an airline. Discrete. The number of suitcases lost must be a whole number. 2) The height of corn plants. Continuous. The height of corn plants can take on infinitely many values (any decimal is possible). 3) The number of ears of corn produced. Discrete. The number of ears of corn must be a whole number.

Classify each set of data as discrete or continuous. 4) The number of green M&M's in a bag. Discrete. The number of green M&M's must be a whole number. 5) The time it takes for a car battery to die. Continuous. The amount of time can take on infinitely many values (any decimal is possible). 6) The production of tomatoes by weight. Continuous. The weight of the tomatoes can take on infinitely many values (any decimal is possible).

Homework Using functions and the analysis of Graphical Information: P22 #1 – 8, 10