NEW DEMO
Basics of Graphs
Basic Properties of 2 Dimensional Graphs
This demo can be used for elementary geometry, pre-calculus, or as a calculus refresher on function properties.
We will assume that a user is familiar with Cartesian coordinates. As a refresher here is a brief description followed by resources for more details. Cartesian coordinates are a system used to describe the position of points in a plane using perpendicular axis lines that meet at a point called the origin. In a two-dimensional plane, a point's position is described by its distance from the origin along the x-axis and y-axis, typically written as (x, y). This system was proposed by the French philosopher and mathematician René Descartes in the 17th century and is the foundation of analytical geometry. Resources: Cartesian coordinates of the plane, Cartesian coordinates description, or, Cartesian plane. There are a variety of resources on the web.
The figure below is a typical example of a graph for this demo.
A graph has many distinguishing properties. In this demo we focus on basic properties
- Intercepts: points where a line or curve intersects the coordinate axes in a plane Specifically, the x-intercept is the point where the line or curve crosses the x-axis, and the y-intercept is the point where it crosses the y-axis.
- Slopes: regions where the graph is increasing or decreasing.
- Jumps:A jump on a graph (also known as a jump discontinuity) is a point where the left-hand limit and the right-hand limit exist but are not equal. This can involve a missing point (or hole) that causes the graph to 'jump' from one value to another, creating a gap in the graph where the trace of the graph is not continuous at that point.
- Domain: When looking at a graph, the domain is all the values of the graph from left to right.
- Range: The range in math is the difference between the highest value and the lowest value in a data set.
To illustrate the the features of the graph Basic Graph above click on the thumbnail images below which high light its features.
IMAGES: =============>
For practice on identifying various properties of basic graphs and related features CLICK here.
Next we we have several EXERCISES to help sharpen your recognition of features of a basic graph.
EXERCISES:=============> Exercise 1 ,<===> Exercise 2 ,<===> Exercise 3 ,<===> Exercise 4 .
Check your solution to the exercises by viewing the thumbnail images bellow. (The images are not in a particular order like the Exercises.)
Notes:
This demo is a modification of a demo in the project Demos with Positive Impact , National Science Foundation's Course, Curriculum, and Laboratory Improvement Program under grant DUE 9952306, managed by David R. Hill and Lila Roberts. The project was based on submitted ideas from instructors. The original demo appeared in 2006.
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David R. Hill, 4/18/2025