The function f is a rational function.
Since the function has a horizontal asymptote given by
y = 1
then the only possible relationship between the degree of the numerator, N, and the degree of the denominator, D, is as given below
[tex]\begin{gathered} N=D \\ \text{and } \\ y=\frac{a}{b}=1 \\ \text{ Where} \\ a\text{ is the leading coefficient of the numerator} \\ b\text{ is the leading coefficient of the denominator} \end{gathered}[/tex]
With these conditions, we can eliminate option B.
This is because in the case of option B, 1 = N ≠ D = 2
Of all the remaining options, only the function in the case of option C,
has vertical asymptotes at x = -7 and x = 5. Which implies that the domain of f in option C is given by
Dom(f) = (-∞,-7) U (-7, 5) U (5, ∞ )
Hence, the correct choice is option C
