Answer
a) $f(x) = \frac{2x+7}{x-1}$
b) Refer to graph.
Work Step by Step
Note: The graphing utility used is geogebra ( https://www.geogebra.org/calculator )
a) We need to plot:
i) A function whose denominator will be $0$ at $x=1$, (for vertical asymptote) and not simplify by $x-1$
ii) A function whose leading coefficients of numerator and denominator are in a ratio $2:1$, with numerator having the same degree as denominator
$\implies$ This is due to the fact that if the degrees of the polynomials in the numerator and denominator are equal, then the horizontal asymptote is at $y = $ the ratio of the leading coefficients.
$\implies$i) $x-1$ is the denominator ($1-1=0$)
$\implies$ $2x-n$ is the numerator.
Let $n = 7$, arbitrarily.
$\implies$ The required function is: $f(x) = \frac{2x+7}{x-1}$
