find all vertical asymptotes of the following function.\n\n$f(x)=\\frac{x - 9}{2x^{2}-26x + 84}$\n\nanswer…

find all vertical asymptotes of the following function.\n\n$f(x)=\\frac{x - 9}{2x^{2}-26x + 84}$\n\nanswer attempt 1 out of 2\n\nno vertical asymptotes\nno vertical asymptotes\none vertical asymptote\ntwo vertical asymptotes

find all vertical asymptotes of the following function.\n\n$f(x)=\\frac{x - 9}{2x^{2}-26x + 84}$\n\nanswer attempt 1 out of 2\n\nno vertical asymptotes\nno vertical asymptotes\none vertical asymptote\ntwo vertical asymptotes

Answer

Explanation:

Step1: Factor the denominator

Factor (2x^{2}-26x + 84). First, factor out a common factor of (2): (2(x^{2}-13x + 42)). Then factor the quadratic (x^{2}-13x + 42=(x - 6)(x - 7)). So the denominator is (2(x - 6)(x - 7)).

Step2: Set the denominator equal to zero

Set (2(x - 6)(x - 7)=0). Using the zero - product property, (x-6 = 0) gives (x = 6) and (x - 7=0) gives (x = 7).

Step3: Check for common factors with the numerator

The numerator is (x - 9). Since (x-9) has no common factors with ((x - 6)) or ((x - 7)) (i.e., there is no value of (x) for which (x-9=x - 6) or (x-9=x - 7)).

Answer:

Two Vertical Asymptotes ((x = 6) and (x = 7))