Answer:
The rational function that might have the given graph is
.
Step-by-step explanation:
This graph shows a rational function whose numerator is a first order polynomial and denominator is a second order, due to the presence of vertical asymptotes at
and
. The lead coefficient of the numerator must be 1, since horizontal asymptote must be
and intercept must be
, since
.
Then, we conclude that a rational function that might have the graph is:
(1)
We present the proof that given function is appropriate.
Given:
The two functions are:


To find:
The statement that best compares the graph of g(x) with the graph of f(x).
Solution:
The horizontal stretch is defined as:
...(i)
If
, the function f(x) is horizontally stretched by factor
.
If
, the function f(x) is horizontally compressed by factor
.
We have,


Using these functions, we get
...(ii)
On comparing (i) and (ii), we get

Since
, the function f(x) is horizontally stretched by factor
.
Hence, the correct option is D.
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