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Solution :

The graph of f has a slant asymptote y=x+4 and a vertical asymptote at x=5 , hence f(x) may be written as `f(x)=(x+4)+(a)/((x-5))`, <br> where a is a constant to be determined using the fact that `f(2)=0` since f has a zero at x=2. <br> `f(2)=(2+4)+(a)/(2-5)=0:. a=18` <br> Hence f(x) is given by `f(x)=(x+4)+(18)/(x-5)=(x^(2)-x-2)/(x-5)` <br> Check the characteristics of the graph of f shown below. <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/CEN_GRA_C06_S01_028_S01.png" width="80%">