Chapter 3 Graphs and Functions

Chapter Sections 3.1 – Graphs 3.2 – Functions 3.3 – Linear Functions: Graphs and Applications 3.4 – The Slope-Intercept Form of a Linear Equation 3.5 – The Point-Slope Form of a Linear Equation 3.6 – The Algebra of Functions 3.7 – Graphing Linear Inequalities Chapter 1 Outline

§ 3.2 Functions

Understand Relations Dependent and Independent Variables For an equation in variables x and y, if the value of y depends on the value of x, then y is the dependent variable and x is the independent variable. Relation, Domain, Range For an equation in variables x and y, if the value of y depends on the value of x, then y is the dependent variable and x is the independent variable.

NOT A FUNCTION (Tom can’t be 21 and 22 at the same time) Recognize Functions Function A function is a relation in which each element in the domain corresponds to exactly one element in the range. Persons Tom Bob Mark Bill Ages 21 22 25 20 Persons Tom Bob Mark Bill Ages 21 22 25 20 FUNCTION NOT A FUNCTION (Tom can’t be 21 and 22 at the same time)

Use the Vertical Line Test Graph of Function or Relation The graph of a function or relation is the graph of its set of ordered pairs. Vertical Line Test If a vertical line can be drawn so that it intersects a graph at more than one point, then the graph does not represent a function. If a vertical line cannot be drawn so that it intersects a graph at more than one point, then the graph represents a function.

Vertical Line Test NOT A FUNCTION FUNCTION FUNCTION

Understand Function Notation If an equation involving x as the independent variable and y as the dependent variable defines a function, we say y is a function of x and we write y = f(X). When a function is evaluated, a value is substituted into the function. f(x) = 3x + 2 f(1) = 3(1) + 2 = 5 Therefore, when x is 1, y is 5. The ordered pair (1, 5) appears on the graph of y = 3x + 2.