Question

22Select the correct answer.The domain of function ris(-00,-7) (-7.5) U (5.00), and the value of the function approaches 1 as x approaches --o0 and oo. Which functioncould be function ?

Answer 1

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

`\begin{gathered} N=D \\ \text{and } \\ y=(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}`

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