Question

Question 5 of 10
Which of the following rational functions is graphed below?
10 H
10
10
O A. F(x) =
FIX) *-*
X5
X1
B. Fx) = 6-14-5
(x - 1)(x-5)
c. F(X) = 1
D. F(X) = x+5
-
x + 1

Answer 1

We want to find the equation for the graphed rational function. Notice that the options are not given, so I will try to find the function only from the graph.

The function is:

$f(x) = \frac{(x - 5)}{x - 1}$

How to analyze the graph of a rational function?

The first thing that we can see in the graph is that we have vertical asymptotes at x = 1.

The one in the positive side (of the x range) goes to negative infinity, while the other goes to positive infinity, then the equation will be something like:

$f(x) = \frac{something}{x - 1}$

Such that the asymptotes are caused when the denominator is equal to zero.

We can see that we also have a horizontal asymptote at y = 1.

This means that, as x tends to infinity, our function will tend to 1, so we have something like:

$f(x) = \frac{(x + b)}{x - 1}$

The horizontal asymptote is equal to the ratio of the leading coefficients when both polynomials have the same degree, like here, so we can take the two leading coefficients equal to 1, such that:

y = 1/1 = 1

To find the value of b, we evaluate the function in 0:

$f(0) = \frac{b}{-1} = -b$

And if you look at the graph, you can see that at x = 0 we have:

f(0) = 5

then b = -5

So the function is:

$f(x) = \frac{(x - 5)}{x - 1}$

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

https://brainly.com/question/1851758