Write an equation that has a hole at x = 4 and a vertical asymptote at x = - 3.

Question

Mathematics

Scott Campbell

8 March, 21:50

Write an equation that has a hole at x = 4 and a vertical asymptote at x = - 3.

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Clayton Huffman · Answer 1

This has to be a rational equation in order to have those characteristics ... in other words a fraction. One such equation would look like this:

x^2 - 2x - 8/x^2 - x - 12. When you factor both the numerator and the denominator you get (x-4) (x+2) / (x-4) (x+3). Because the (x-4) is in both the top and the bottom of the fraction, you can cancel them out, which makes that (x-4) a removable discontinuity. The (x+3) exists as a vertical asymptote.