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Graphs and Functions

This chapter explores the concepts of graphs and functions, including relations, dependent and independent variables, recognizing functions, graphing functions, and function notation.

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Graphs and Functions

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  1. Chapter 3 Graphs and Functions

  2. 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

  3. Functions § 3.2

  4. 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.

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

  6. 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.

  7. Vertical Line Test NOT A FUNCTION FUNCTION FUNCTION

  8. Understand Function Notation 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.

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