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CN College Algebra Ch. 2 Functions and Their Graphs 2.1B: Functions

CN College Algebra Ch. 2 Functions and Their Graphs 2.1B: Functions. Goals: Find the domain of a function. Identify the graph of a function. Obtain information from or about the graph of a function. Relation:.

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CN College Algebra Ch. 2 Functions and Their Graphs 2.1B: Functions

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  1. CN College AlgebraCh. 2 Functions and Their Graphs2.1B: Functions Goals: Find the domain of a function. Identify the graph of a function. Obtain information from or about the graph of a function.

  2. Relation: • Relation: A relation is a correspondence between two sets. If x and y are two elements in these sets and if a relation exists between x and y, then we say that x corresponds to y, or y depends on x, and we write either x  y or the ordered pair (x, y).

  3. Function, Domain, Value, Image, Range: • Function: Let X and Y be two nonempty sets. A function from X into Y is a relation that associates with each element of X exactly one element of Y. • The set X is the domain of the function. For each element x in X, the corresponding element y in Y is the value of the function at x, or the image of x. The set of all images of the elements in the domain is the range of the function.

  4. Independent Variable, Dependent Variable: • For a function y = f(x), the variable x is the independent variable, because it can be assigned any of the numbers from the domain. The variable y is the dependent variable, because its value depends on x. The independent variable is also called the argument of the function.

  5. Graph of a function/Vertical-line agent: • Graph of a function: When a function is defined by an equation in x and y, the graph of thefunction is the graph of the equation, that is, the set of points (x, y) in the xy-plane that satisfies the equation. • Vertical-line test: A set of points in the xy-plane is the graph of a function if and only ifevery vertical line intersects the graph in at most one point.

  6. Assignments: • Class Work: C & V #2, 4, 5, & 8. • Homework: 2.1 Exercises #33-71 (odds), except #45 and 65.

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