Which statement correctly uses limits to determine a vertical asymptote of g of x is equal to the fraction with numerator negative 7 open paren x minus 5 close paren squared open paren x plus 6 close paren and denominator open paren x minus 5 close paren times open paren x plus 5 close paren ?

For x ≠ 5, cancel the common factor (x − 5) to get g(x) = −7(x − 5)(x + 6)/(x + 5). At x = −5, the numerator approaches 70, a positive number, while the denominator approaches 0. From the left, x + 5 is negative, so g(x) approaches negative infinity; from the right, x + 5 is positive, so g(x) approaches positive infinity. Thus x = −5 is a vertical asymptote, as stated in choice C.

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