Question

which of the following rational functions is graphed below

Answer 1

Answer:

D

Step-by-step explanation:

This graph shows two vertical asymptotes, one at x = +3, the other at x = 4.  Thus, we omit the first two answer choices.  Next, we substitute 0 for x and determine the y value in Answer Choice C:  F(0) = 0.  Does the graph go through (0, 0)?  Yes, it does.  Next, evaluate F at x = 3.5 (halfway between x =  3 and x = 4); that is, evaluate function D at x = 3.5.  Does the y value come out to be -4 as shown in the graph?  Yes, it does.    So D is the correct function to match this graph.

Answer 2

Considering the vertical asymptotes of the function, and it's behavior, it is found that the rational function graphed below is given by:

D. $f(x) = \frac{1}{(x - 3)(x - 4)}$

What are the vertical asymptotes of a function f(x)?

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.

In this problem:

• There are vertical asymptotes at x = 3 and x = 4, hence the denominator of the function is (x - 3)(x - 4).

• At x = 3.5, we have that f(x) is approximately 4, hence the numerator is 1.

Thus, the correct option is:

D. $f(x) = \frac{1}{(x - 3)(x - 4)}$

More can be learned about vertical asymptotes at https://brainly.com/question/11598999