find the vertical asymptote(s) of the graph of the function.\nf(x)=\\frac{4 - x}{(x - 5)(x + 4)}\nselect the…

find the vertical asymptote(s) of the graph of the function.\nf(x)=\\frac{4 - x}{(x - 5)(x + 4)}\nselect the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.\noa. the function has one vertical asymptote, □\n(type an equation.)\nob. the function has two vertical asymptotes. the leftmost asymptote is □ and the rightmost asymptote is □\n(type equations.)\noc. the function has no vertical asymptotes.

find the vertical asymptote(s) of the graph of the function.\nf(x)=\\frac{4 - x}{(x - 5)(x + 4)}\nselect the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.\noa. the function has one vertical asymptote, □\n(type an equation.)\nob. the function has two vertical asymptotes. the leftmost asymptote is □ and the rightmost asymptote is □\n(type equations.)\noc. the function has no vertical asymptotes.

Answer

Explanation:

Step1: Find the values that make the denominator zero

Set ((x - 5)(x + 4)=0). Using the zero - product property (ab = 0) implies (a=0) or (b = 0). So (x-5=0) gives (x = 5), and (x + 4=0) gives (x=-4).

Step2: Check for common factors with the numerator

The numerator is (4 - x). There are no common factors between (4 - x) and ((x - 5)(x + 4)).

Answer:

The leftmost asymptote is (x=-4) and the rightmost asymptote is (x = 5). So for option B, the leftmost asymptote is (x=-4) and the rightmost asymptote is (x = 5).