How many vertical asymptotes does the equation $y=\frac{x-1}{x^2+6x-7}$ have?
+23252 To determine vertical asymptotes, you must first factor both the numerator and denominator and cancel
out those factors which are found in both the numerator and denominator.
y = (x - 1) / (x2 + 6x - 7) = (x - 1) / [ (x - 1)·(x + 7) ] = 1 / (x + 7)
Because there is a factor of (x + 7) remaining in the denominator, there is one vertical asymptote,
at x = -7.
The factor (x - 1) does not give a vertical asymptote, instead, it creates a "hole" in the graph at x = 1.
