Respuesta :

A function is said to be rational , if function possess variable in numerator as well as denominator or either in numerator or  in Denominator because coefficient of variable either in numerator or denominator can be zero.

Now coming to function described in the graph

It has a vertical Asymptote given by :

x=2.

So, the curve will contain (x-2) in the denominator.

We don't need to graph different function on desmos.

By looking at options we can say which function is represented in the graph.

Option (B), F(x) = [tex]\frac{1}{x-2}[/tex] is appropriate choice.  


MrRoyal

The rational function is (b) f(x) = 1/x - 2

How to determine the rational function?

From the graph, we have the following highlights.

  • The vertical asymptote is x =2
  • The horizontal asymptote is y =0

The above means that, the equation of the function is:

y = a/b

Where a is a constant;

Assume a = 1.

So, we have:

y = 1/b

b is calculated from the vertical asymptote

x  = 2

Subtract 2 from both sides

x - 2 = 0

So, we have:

b = x - 2

Substitute x - 2 for b in  y = 1/b

y = 1/x - 2

Hence, the rational function is (b) f(x) = 1/x - 2

Read more about rational functions at:

https://brainly.com/question/1851758

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