+ Represent Relations and Functions

+ Relation A relation is a mapping, or pairing, of input values with output values. The set of input values in the domain. The set of output values is the range.

+ Representing Relations A relation can be represented in the following ways:  Ordered pairs  Table  Graph  Mapping Diagram

+ Ordered Pairs (-2, 2), (-2, -2), (0, 1), (3,1) Domain (the x values): {-2, 0, 3} Range (the y values): {-2, 1, 2}

+ Table xy Domain: {-4, -2, 1, 4} Range: {2, 6, 7}

+ Graph Domain: {-2, -1, 1, 2, 3} Range: {-3, -2, 1, 3}

+ Mapping Domain: {-2, -1, 1, 2, 3} Range: {-3, -2, 1, 3}

+ Is the relation a function?  A relation is a function if each input has exactly one output… “the x’s can’t repeat”

+ Function?? Function Not a Function

+ Vertical Line Test  A relation is a function if and only if no vertical line intersects the graph of the relation at more than one point. Function Not a Function

+ Equations in Two Variables  An equation in two variables is an equation such as y = 3x - 5  “x “ is the input variable and is called the independent variable. It represents the independent quantity.  “y” is the output variable and is called the dependent variable. It represents the dependent quantity. “y depends on x”

+ Solution  An ordered pair (x, y) is a solution of an equation in two variables if substituting x and y in the equation produces a true statement. Ex: (2, 1) is a solution to y = 3x – 5 because 1 = 3(2) – 5  The graph of an equation in two variables is the set of all points (x, y) that represent solutions of the equation.

+ Linear Functions  A linear function can be written in the form y = mx + b  The graph of a linear function is a line  y = mx + b ~ x-y notation  f(x) = mx + b ~ function notation (‘f of x” or “the value of f at x”) Ex: f(x) = 5x + 8 f(-4) = 5(-4) + 8 = -12 The value of the function at x = -4 is -12.

+ Discrete and Continuous Functions  The graph of a discrete function consists of separate points.  The graph of a continuous function is “unbroken”

+ Slope Watch and listen to the following links: Introduction to slope Parallel and Perpendicular Lines