Description

A useful application of Algebra is to explore the Rectangular (Cartesian) System including how to graph line, functions and inverse functions. This topic explores the Rectangular (Cartesian) Coordinate System and graphing linear equations in two variables. We continue by exploring slopes of lines (including parallel and perpendicular lines), the distance and midpoint formulas; given information, writing equations in the Point-Slope, Slope-Intercept and the General Forms; exploring relations, functions, function motation, and the algebra of functions as well as inverse functions.

Sections of this topic include:

1. The Rectangular Coordinate System; Graphing Linear Equations in Two Variables

   One of the greatest applications of Algebra is that of plotting points and exploring graphs. So, we begin with the Rectangular coordinate system and graphing linear equations in two variables. Groups within this section include: plotting points in the rectangular coordinate system; determining the quadrant a point is in; graphing equations by plotting points; determining if a point lies on a line; graphing equations by using the x- and y- intercepts; and translating phrases into equations then graphing.

2. The Slope of a line; distance and Midpoint Formulas.

   With an understanding of the rectangular coordinate system, we next to concepts involving formulas. We investigate how to find a slope of a line given two points, finding the distance between two points or the midpoint of the line segment that connects to points. Groups within this section contain: finding the slope of a line given two ordered pairs; graphing lines using slopes, horizontal lines, vertical lines; using slopes to determin if points are collinear; determining a slope from a graph; finding the distance between two points; finding the midpoint between two points; determining if lines are perpendicular, parallel, or neither.

3. Point-Slope, Slope-Intercept, and the General Form of the Equation of a Line

   Building on the equations of lines, we next investigate forms of lines such as the point-slope, slope-intercept and general form of an equation of a line. We also investigate given enough information, finding these equations of lines. Groups within this section contain: writing equations of a line given a point and a slope; writing equations of a line given two points; writing equations in slope-intercpet form given a slope and y-intercept; writing equations that satisfy conditions; writing equations of lines from a graph.

4. Relations, Functions, and Function Notation

   We next explore the concepts of relations, functions and the related function notation for functions. Groups within this section include: determining if a relation is a function; domain and range; determining if a relation is a function; finding the domain; evaluating functions.

5. The Algebra of Functions. Inverse Functions

   Much like other expressions in Algebra, we are curious how to perform arithmetic operations with functions as well as finding inverse functions. Groups within this section include: the algebra of functions; finding composite functions; finding an inverse of a relation, domain and range.