Respuesta :

Answer:

Figure 2

Step-by-step explanation:

We are given the function [tex]f(x)=\frac{1}{x-1}[/tex].

Now, when x = 1, we have that,

[tex]f(x)=\frac{1}{1-1}[/tex] i.e. [tex]f(x)=\frac{1}{0}[/tex] i.e. [tex]f(x)\rightarrow\infty[/tex].

Also, when x = -1, we have that,

[tex]f(x)=\frac{1}{-1-1}[/tex] i.e. [tex]f(x)=\frac{1}{-2}[/tex].

Further, when f(x) = -1, we have that,

[tex]-1=\frac{1}{x-1}[/tex] i.e. [tex]-x+1=1[/tex] i.e. [tex]x=0[/tex].

So, it is clear from the given options that the second figure is the correct graph of the function [tex]f(x)=\frac{1}{x-1}[/tex].

Hence, figure 2 is the correct option.

The graph of the given function is shown by option B) and this can be determined by using the substitution method.

Given :

Function  --  [tex]\rm f(x) = 1/(x-1)[/tex]

The following steps can be used in order to determine the graph of the given function:

Step 1 - The substitution method can be used in order to determine the graph of the given function.

Step 2 - Substitute the value of (x = 0) in the given function.

[tex]\rm f(0) = \dfrac{1}{0-1}[/tex]

f(0) = -1

Step 3 - Substitute the value of (x = 1) in the given function.

[tex]\rm f(1) = \dfrac{1}{1-1}=\infty[/tex]

Step 4 - Susbtitute the value of (f(x) = 1) in the given function.

[tex]1=\dfrac{1}{x-1}[/tex]

x = 2

Step 5 - Substitute the value of (f(x) = -1) in the given function.

[tex]-1=\dfrac{1}{x-1}[/tex]

x = 0

Therefore, the correct option is B).

For more information, refer to the link given below:

https://brainly.com/question/14375099

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