Respuesta :

profantoniofonte

Answer:

c)

[tex]f(x)=\frac{1}{x(x+4)}[/tex]

Step-by-step explanation:

Hi there!

This is a Rational Function. The process of graphing it takes a lot more hard work than graphing other functions like linear, quadratic, modulus, and so on.

Here a list on how to proceed

First

1) Find the point of intersections by calculating the zeros of the function on the Numerator. In this case, we just have a 1 on top, so our graph won't intercept x-axis.

2) Calculate the vertical asymptotes by calculating the zeros of the function in the denominator, x²+4x=0 S=(0,-4) on green on the graph below.

3) Construct the table of values for x, and y

4) Trace the graph

Ver imagen profantoniofonte
facundo3141592

By analyzing the asymptotes on the graph, we conclude that the correct option is C.

How to determine the rational function graphed?

To do it, we need to see at which x-values we have asymptotes. These are the values of x where the denominator becomes equal to zero.

Here we can see that we have asymptotes at:

x = 0 and x = -4

Then the denominator must be a polynomial with roots at x = 0 and x = -4, this is written as:

(x - 0)*(x - (-4)) = x*(x + 4)

So the rational function is something like:

[tex]f(x) = \frac{1}{x*(x + 4)}[/tex]

So the correct option is C.

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

https://brainly.com/question/1851758

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