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What's the Vertical Line Test?

Definition: Vertical Line Test

Summary

  1. We can draw more than one imaginary vertical lines
  2. The graphed equation should not pass through any dashed line more than once if it's a function
  3. For the example on the left, any imaginary vertical lines will only pass through the graphed line one time, so the line is a function
  4. For the example on the right, at least one imaginary vertical line passes through the graphed line three times, so the line is NOT a function

Notes

    1. So we draw a dashed vertical line to see if our graphed equation passes through it more than once
    2. If it passes through the vertical line more than once, the equation is NOT a function
    1. To show that the line is imaginary, make it a dashed line
    1. The imaginary line is the dashed line drawn on the graph
    1. The imaginary line is the dashed line drawn on the graph
    2. In other words, if the graphed equation passes through the dashed vertical line more than once, the equation is NOT a function
    1. The imaginary line is the dashed line drawn on the graph
    2. In other words, if the graphed equation passes through the dashed vertical line two or more times, the equation is NOT a function
    1. The imaginary line is the dashed line drawn on the graph
    2. In other words, if the graphed equation passes through the dashed vertical line two or more times, the equation is NOT a function
    3. Failing the vertical line test means that the graphed equation is NOT a function
    1. To show that the line is imaginary, make it a dashed line
    1. If the graphed equation crosses through the dashed vertical line two or more times, the equation will NOT be a function
    1. If the graphed equation crossed through the dashed vertical line two or more times, the equation would NOT be a function
    1. The first graphed equation never crosses through the dashed vertical line more than one time, so it's a function!
    1. To show that the line is imaginary, make it a dashed line
    1. Remember, we just care about whether the dashed vertical line passes through the graphed equation more than once
    1. At this point, we see the graphed equation cross through the dashed vertical line
    1. Remember, if the graphed equation crosses through the dashed vertical line two or more times, the equation will NOT be a function
    1. Remember, if the graphed equation crosses through the dashed vertical line two or more times, the equation will NOT be a function
    2. Our imaginary vertical line crossed paths with the graphed equation three times, so it's NOT a function
    1. We simply draw a dashed vertical line to see if our graphed equation passes through it more than once
    2. If it does, then the graphed equation is NOT a function