Chapter 2: Linear Equations and Functions Section 2.1: Represent Relations and Functions

Relation – a mapping or pairing of input values with output values. Domain – the set of input values. Range – the set of output values. Function – a relation for which each input has exactly one output. *If any input of a relation has more than one output, the relation is not a function.

Representing Relations A relation can be represented in the following ways: Ordered Pairs (-2, 2), (-2, -2), (0, 1), (3, 1) Table xy

Graph Mapping Diagram

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.

Equation in two variables – many functions can be described by an equation in two variables, such as y = 3x – 5. Independent variable – the input variable (in this case, x). Dependent variable – the output variable (in this case, y). It is called a dependent variable because its value depends on the value of the input variable.

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. Graph – the graph of an equation in two variables is the set of all points (x, y) that represent solution of the equation.

Example 1: Consider the relation given by (3, 2), (-1, 0), (2, -1), (-2, 1), (0, 3). a)Find the domain and range. Domain: {-2, -1, 0, 2, 3} Range: {-1, 0, 1, 2, 3} b) Represent the relation using a mapping diagram.

Example 2: Is the relation a function? Explain. a)(-5, 4), (-1, 0), (3, -1), (3, -2) No Input 3 has two different outputs. b)(-3, 5), (0, 5), (2, 1), (6, -8) Yes Each input has exactly one output.

Example 3: Use the vertical line test to tell whether the relation is a function. a)b) Yes No

HOMEWORK (Day 1) pg. 76 – 77; 3 – 23

Linear function – a function that can be written in the form y = mx + b where m and b are constants. The graph of a linear function is a line. Function notation – by renaming y as f(x), you can write y = mx + b using function notation.

Domains in Real Life The domain of a function is all real numbers because there is an output for every real number x. In real life, you may need to restrict the domain so that is reasonable in the given situation.

Graphing Equations in Two Variables To graph an equation in two variables, follow these steps: 1)Construct a table of values. 2)Plot enough points from the table to recognize a pattern. 3)Connect the points with a line or a curve.

Example 4: Tell whether the function is linear. Then evaluate the function when x = -3. a)f(x) = -2x Not linear 59 b)g(x) = 12 – 8x Linear 36

HOMEWORK (Day 2) pg. 78; 34 – 39

Example 5: Graph the following equations. a)y = 3x – 5 b) y = ½ x + 2 c)y = -4x – 1

HOMEWORK (Day 3) pg. 77; 25 – 33