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BTW, with regard to Quaid's response, vertical asymptotes do not necessarily occur whenever a denominator has value zero. This condition alone only implies the function to be undefined.
The line x = r is a vertical asymptote of function, f, if the limit of f as x approaches r does not exist (i.e., f tends toward +/- infinity as x approaches r).
Consider f(x) = (x2 - 1) / (x - 1). This function is undefined for x = 1, but the limit as x approaches 1 is 2. To see this, notice that factoring x2 - 1 gives,
f(x) = (x+1)(x-1)/(x-1) = x + 1 ; x not = 1. Hence the graph of f is just a line with a missing point at (1, 2). no asymptote.
Rich
BTW, with regard to Quaid's response, vertical asymptotes do not necessarily occur whenever a denominator has value zero. This condition alone only implies the function to be undefined.
The line x = r is a vertical asymptote of function, f, if the limit of f as x approaches r does not exist (i.e., f tends toward +/- infinity as x approaches r).
Consider f(x) = (x2 - 1) / (x - 1). This function is undefined for x = 1, but the limit as x approaches 1 is 2. To see this, notice that factoring x2 - 1 gives,
f(x) = (x+1)(x-1)/(x-1) = x + 1 ; x not = 1. Hence the graph of f is just a line with a missing point at (1, 2). no asymptote.
Rich
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