Ellen described the asymptotes of the two functions correctly, and she correctly rewrote g(x) as a transformation of f(x). Then the correct option is B.
The complete question is attached below.
An asymptote is a line that constantly reaches a given curve, but does not touch at any infinite distance.
Ellen is exploring the key features of the functions f(x) and g(x) are given below.
[tex]\rm f(x) = \dfrac{x + 2}{x - 3}\ and \ g(x) = \dfrac{2x -1}{x - 3}[/tex]
She says that the graphs of the two functions will have the same vertical asymptote but different horizontal asymptotes because she can define function g as a transformation of function f and g(x) = f(x) + 1.
Then the value of g(x) = f(x) + 1 will be
[tex]\rm g(x) = f(x) + 1\\\\\\ \dfrac{2x -1}{x - 3} = \dfrac{x + 2}{x - 3} + 1\\\\\\ \dfrac{2x -1}{x - 3} = \dfrac{x + 2 + x - 3}{x - 3} \\\\\\ \dfrac{2x -1}{x - 3} = \dfrac{2x - 1}{x - 3}[/tex]
Then we have
Ellen described the asymptotes of the two functions correctly, and she correctly rewrote g(x) as a transformation of f(x).
Then the correct option is B.
More about the asymptote link is given below.
https://brainly.com/question/17767511
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