What is the Vertical Line Test?
The vertical line test is a method used in math to check if a graph is a function. A graph is a function only if it has one output, y, for each input, x.
How to use the Vertical Line Test?
To use the vertical line test, draw a vertical line through the given graph. In the graph below, the vertical line was drawn at x = 2.
Now look at the graph and determine how many times the line passes through the graph. In this case, the line passes through the graph only once, therefore the graph is a function. There is only one output, y, for each input, x.
A graph is not a function, if the vertical line passes through the graph more than once. In the example below, the vertical line is drawn at x = -1. It passes through the graph at the points (-1,4) and (-1,-4). This shows that there are two outputs, y, for the input, x.
Since there are two points that the vertical line passes through and there is more than one output for each input, it does not pass the vertical line test. It is not a function.
Sample Math Problems
Question 1:
Use the Vertical Line Test to determine if the graph is a function.
Answer:
To solve this problem, first draw a vertical line through the graph.
The vertical line is drawn at x = 2 and only passes through the graph once. Since there is only one output y, for each input, x, this graph is a function.
Question 2:
Use the Vertical LineTest to determine if the graph is a function.
Answer:
To solve this problem, first draw a vertical line through the graph.
The vertical line is drawn at x = 3. It passes through the graph at two points. Since there are 2 outputs, y, for each input, x, this graph is not a function.
Question 3:
Use the Vertical Line Test to determine if the graph is a function.
Answer:
Draw a vertical line through the graph.
The vertical line is drawn at x = -2. It passes through the graph only once. Since there is only one output, y, for each input, x, this graph is a function.
Question 4:
Use the Vertical Line Test to determine if the graph is a function.
Answer:
Draw a vertical line through the graph.
The vertical line is drawn at x = -4 and passes through the graph at 2 points. Since there are two outputs y, for each input, x, this graph is not a function.
