Which of the following rational functions is graphed below ?

By analyzing the vertical asymptotes, we will see that the correct option is A.

We know that the vertical asymptotes in the graph of a rational function are at the values of x that make the denominator equal to zero.

Here, we can see that we have the asymptotes at x = -2 and at x = 5, so we can assume that the denominator is of the form:

d(x) = (x + 2)*(x - 5)

Now if you look at the options, there is only one that has this denominator, which is A:

If you want to learn more about rational functions, you can read:

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Option A.

Step-by-step explanation:

If you look closely at the graph, we can notice that the function is not defined at two different points.

If you look at functions B and C, you will notice that both functions are not defined at just one point. The function B is not defined at x= -5/2 and function C is not defined at x=-5. Both options are discarded, given that our function should not be defined at two fiferent points.

Now, if you look closely at the graph you will notice that the function sketched is not defined at x=5 and x=-2.