Vertical Line Test
Vertical line test is a test that tells us whether a given graph is a function or not. Any relation is considered a function if any vertical line drawn along the graph of the relation intersects the graph only at one point. We know that for any relation to be considered a function it only has one output for every input. And thus, if the vertical line cuts the graph of the given relation more than once then it is not a function.
In the image added below, a vertical line drawn to y = f(x)(figure 1) cuts the graph at only one point, and thus, y = f(x) is a function because it follows the vertical line test. For instance, the graph of y = f(x)(figure 2) is not a function because a vertical line drawn cuts the graph at two points and it fails the vertical line test.
Vertical Line
Vertical line is a line that is perpendicular to the base of any geometrical object and generally, we state the bottom of the object as a base. In simple words, we define a vertical line as a line that is perpendicular to the horizontal line. In context to the cartesian coordinate system, vertical lines are defined as lines that are parallel to the y-axis or perpendicular to the x-axis. A vertical line always goes from top to bottom and is also called a standing line.
Various examples where we observe vertical lines are the lines joining the base of the rectangle, square, etc. The vertical lines are very useful for solving and explaining various geometrical problems. This article explores the topic of Vertical Lines including its subtopics like its definition, diagram, relation with other lines, etc. So, let’s learn about the vertical lines in detail in this article.
Table of Content
- Vertical Line Definition
- Vertical Line on Coordinate Plane
- Equation of Vertical Line
- Example of Vertical Lines
- Slope of Vertical Line
- Properties of Vertical Lines
- Difference between Horizontal Line and Vertical Line
- Vertical Line Test
- Vertical Line of Symmetry
- Vertical Line Summary
- Vertical Line Examples
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