Find the vertical asymptotes and holes of .
Hint
Where does the denominator equal 0? Can it be canceled out?
Answer
There is a vertical asymptote at x = -7.
Find any vertical asymptotes or holes of .
The denominator factors to (x + 1)(x – 3).
There is a hole at x = -1 and a vertical asymptote at x = 3.
Factor fully, strike out similar terms, and asymptotes are all that's left in the bottom.
There is a hole at x = 2.
Finish factoring the denominator, then check if anything cancels out.
There are vertical asymptotes at x = -3, -2, and 1.
Find any vertical asymptotes and holes of .
Where can the denominator equal zero on the x-axis?
There are no holes and no vertical inequalities. The denominator cannot equal ever equal zero.
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