Describe the vertical-line test for functions. Why is the vertical-line test a valid method for testing if a graph is a function or not. (Hint: What is the connection between the vertical-line test and the definition of a function, i.e. what does a single vertical line represent, and how does this test if a graph is or is not a function?)
Devin
a function has only 1 y value for each discrete x value. Assuming that on your graph y=F(x), then a true function will have only 1 x value at any given point. By drawing a vertical line, you are visually trying to see if at any point there are more than 1 correct value for X. An example would be Y=x. Mathematically, we know that for any value x, there is only one solution. That is, only one corresponding y value. Graphically, this is a diagonal line and we know that anywhere we draw a vertical line, it will only intersect with the graph of our function one time.
Alternatively, the equation y=square root(x) is not a function. This we know because a negative times a negative is positive, so the square root of four is both 2 and negative 2. In this sense, not a function because there are 2 solutions to that x-value. If you graph this, it is essentially a parabola turned on its side, so a vertical line on any positive would intersect the graph twice.
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Vertical Line Test Definition