Explain why a graph that fails the vertical-line test does not represent a function

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Trevor Baxter

Mathematics

4 October, 08:48

Explain why a graph that fails the vertical-line test does not represent a function

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Brown · Answer 1

For any given y value, there can only be one x value. Let's consider a graph with a line that curves and intersects x=2 twice. This would mean that if you plug 2 into the function you would get two answers. However, this is not possible as plugging in any value to x will result in only one answer. For example, if y = 4x + 3, no matter how many times I plug a number in there, I'm always going to get the same y value, and this is true for all real functions.