Relations, Functions, and Linear Equations.

Your teacher is asking you the difference between a relation and a function, or somebody is telling you that all functions are relations; but not all relations are functions. Why? How do I determine that I have a linear equation? What is the importance of the exponents in a linear equation? Is there a way of determining in an easy way that a graph belongs to a function? Up in the upper right side of the lesson you have the MARKER TOOLS menu to highlight important sections of the problems, and come back to them. Below the screen displaying the lesson you will find several definitions that might be wise to review before going over the lesson itself.

This lesson will answer all those questions. You will learn the different representations of a relation, and the definition of a function. You will be able to figure out this using the mapping, the set of points, or the graph belonging to a relation. To find out if a graph is a function or not; you will use the Vertical Test. Go ahead and embark your self in a math discovering adventure!

Lesson's Content

Lesson In PDF Format (no animations)

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Lesson's Glossary

Abscissa: It is the x-coordinate in a ordered pair (x,y).

Coordinate axes:  The x - and y - axes in the coordinate plane.

Coordinate plane:  Defined by two number lines that are perpendicular and for which the intersection point is the origin (0,0); and the horizontal axis is the x-axis and the vertical axis is the y-axis.

Coordinate of a point:   The number that is paired a point in the number line.

Coordinates of a point:  The abscissa and ordinate of the point, written as an ordered pair of
numbers.

Domain of a function:  All the values for the independent variable in a function.

Domain of a variable:  All the numbers in a set that are represented for the variable.

Equation: A mathematical statement that has to expressions joined by the = sign. It has the right side of the equation (expression1) and the left side of the equation (expression 2)

Equivalent equations: An equation that when solved have the same solution set over a given domain.

Equivalent expressions:  All expressions that represent the same number for any value of the variable that they contain.

Functional notation:  A notation used to define a function; for example, f(x) = 7x + 100.

Graph of an equation in two variables: All the points that may be graph from the solution set of the equation.

Graph of a function:  The solution set graphed for the function in the given domain.

Graph of a number:   The location of a point pairedwith a number in the number line.

Graph of an ordered pair:  The location in the coordinate plane associated with an ordered pair of real numbers.

Graph of a relation:  The graphs of all the ordered pairs that form the relation.

Horizontal axis:  The horizontal number line in a coordinate plane. Also called the x-axis.

Linear equation in two variables:  All equivalent equations to the one in the form of ax + by = c, where a, b, and c are in the set of the real numbers and a and b can't be zero at the same time. The graph is a straight line.

Linear function:  A function of the form: f(x) = mx + b.

Linear equation:  Any equation with all exponents = 1 regardless of the form the equation is represented.

Linear term:   A term of degree one.

Ordered pair:   A pair of numbers for which the order of the numbers is important; (2, -3) is an ordered pair.

Ordinate:  The y-coordinate in an ordered pair of the coordinate plane.

Origin:   The location of the zero point in a number line.

Sides of an equation:  The two expressions at both sides of the equal sign in an equation. Left and right.

Sides of an inequality: The two expressions at both sides of the inequality sign in an inequality. Left and right.

Solve an equation:  To find the solution, to find the answer, to get to know the value for which a variable stands for.

Standard form of a linear equation:   ax + by = c, where a, b, and c are integers and a and b are not both zero.

Terms:  A form of grouping one or more numerical and/or variable factors by means of multiplication and division.

Variable: A letter used to represent a number. When the variable is part of an equation, it is possible to find the value for which it stands for by solving the equation. This is the solution (s) of the equation.

Variable expression: Any expression containing one or more variables.

x-intercept:  The x-coordinate of a given point for which the graph intersects the x-axis.

y-intercept: The y-coordinate of a given point for which the graph intersects the y-axis.

 

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