Vertical Line Test Game

Vertical Line Test Game
This game is designed to help you master the Vertical Line Test, which is the quickest way to determine if a graph represents a mathematical function. Scroll down for a detailed explanation.
 

 

How to Play the Vertical Line Test Game

1. Analyze the Graph
   When a graph appears in the blue-bordered box, look at its shape. Imagine a vertical line (like a ruler held straight up and down) moving from the left side of the graph to the right.
   

2. Apply the Test
   You are looking for one specific rule:
   It IS a function (YES): If a vertical line touches the graph at only one point at any given time.
   It is NOT a function (NO): If a vertical line touches the graph at two or more points at the same time.
   

3. Cast Your Vote
   Click the YES (Green) or NO (Red) button based on your observation.
   YES: Use this for straight lines (not vertical ones!), “U” shaped parabolas, or wavy curves.
   NO: Use this for circles, sideways “U” shapes, or vertical lines.
   

4. Watch the “Scanner”
   Once you click a button, a red dashed line will sweep across the graph. This is the “Scanner."
   Watch closely: As it moves, notice if it ever overlaps with the blue graph line in more than one spot.
   The game will provide a written Explanation below the graph to tell you exactly why that specific shape passed or failed.
   

5. Check Your Score
   Your Score (correct answers) and Total (attempts) are tracked at the bottom. Click NEXT GRAPH → to clear the board and try a new shape.
   

What is the vertical line test?
The Vertical Line Test is a visual method used to determine if a curve on a coordinate plane represents a function.
In mathematics, a function is defined by a strict rule: for every unique input (x), there must be exactly one output (y). The vertical line test is the easiest way to see if a graph follows that rule.

How to Perform the Test
Imagine taking a vertical line (like a ruler held perfectly upright) and sliding it across the graph from left to right.
Pass: If the vertical line intersects the curve at only one point everywhere on the graph, then the graph is a function.
Fail: If there is any spot where the vertical line intersects the curve at two or more points, then the graph is not a function.

Why It Works
The x-axis represents your inputs. When a vertical line hits a graph in two places, it means that for that specific x value, there are two different y values.

Common Examples
The Parabola (y = x²)
If you have a standard “U-shaped” parabola opening upward, any vertical line you draw will only hit the “U” once.
Verdict: It is a function.

The Sideways Parabola (x = y²)
If the “U” is knocked over on its side, a vertical line will hit both the top “arm” and the bottom “arm” of the curve.
Verdict: It is not a function.

Circles
A circle fails the test almost everywhere. If you draw a vertical line through the center of a circle, it hits the top edge and the bottom edge. Verdict: It is not a function.

This video gives a clear, step-by-step approach to understand the vertical line test.

• Show Video

 

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