Which graph represents the function f(x)=1/x+3-2

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Which graph represents the function f(x)=1/x+3-2

Which graph represents the function f(x)=1/x+3-2

Number 3, because if you replace x for 1 then you get zero. and because it is rise over run then the run is 0. it is the only line with a run of 0

The graph as shown below.

Step-by-step explanation:

Given : The function [tex]f(x)=\frac{1}{x-3}-2[/tex]

We have to plot the graph for the given function [tex]f(x)=\frac{1}{x-3}-2[/tex]

Consider the given function [tex]f(x)=\frac{1}{x-3}-2[/tex]

Domain of function [tex]f(x)=\frac{1}{x-3}-2[/tex]

DOMAIN is set of input values for which the function is real and has defined values.

So, The given function is undefined at x = 3

So, Domain is [tex]x<3\quad \mathrm{or}\quad \:x3[/tex]

RANGE is the set of values of dependent variable for which the function is defined.

Inverse of given function is [tex]y=\frac{3x+7}{x+2}[/tex]

Now, domain of inverse function is [tex]f\left(x\right)<-2\quad \mathrm{or}\quad \:f\left(x\right)-2[/tex]

Now, x intercept and y- intercepts

x intercept where y = 0 and y- intercept where x= 0

Let f(x) = y

Then [tex]y=\frac{1}{x-3}-2[/tex]

Put x = 0

thus y- intercept is [tex]\left(0,\:-\frac{7}{3}\right)[/tex]

Now put y = 0

Then x- intercept is [tex]\left(\frac{7}{2},\:0\right)[/tex]

Now, Calculate the vertical and horizontal asymptotes,

Vertical asymptotes,

Go over every undefined point and check if at least one of the following statements is satisfied.

[tex]\lim _{x\to a^-}f\left(x\right)=\pm \infty[/tex]

[tex]\lim _{x\to a^+}f\left(x\right)=\pm \infty[/tex]

Thus, The vertical asymptotes is x = 3

And For horizontal asymptotes,

[tex]\mathrm{Check\:if\:at\:}x\to \pm \infty \mathrm{\:the\:function\:}y=\frac{1}{x-3}-2\mathrm{\:behaves\:as\:a\:line,\:}y=mx+b[/tex]

We have y = -2 as horizontal asymptotes.

Plot we get the graph as shown below.

[tex]Which graph represents the function f(x)=1/x+3-2[/tex]

files are attached below

[tex]Which graph represents the function f(x)=1/x+3-2[/tex]

[tex]Which graph represents the function f(x)=1/x+3-2[/tex]

To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.

Please see the attached image below, to find more information about the graph

The equation is:

f(x) = 1/x - 1

Domain

All real numbers except for {0}

[tex]Which graph represents the function f(x) = 1/x - 1?[/tex]

It would be the fourth graph, D

Explanation:

When faced with these problems, you can either plot it on your own or you can use a graph generator online.

Step-by-step explanation:

To eliminate ambiguity please use parentheses when typing a function like this one. I'm going to assume that you meant

f(x) = 1 / (x + 3) - 2

Start with the graph of y = 1/x. Its vertical asymptote is the line x = 0. The graph never touches the x-axis.

Translating the entire graph 3 units to the left will give you the function

h(x) = 1 / (x + 3).

Translating the above graph 2 units down will give you the desired function g(x) = 1 / (x + 3) - 2.

Plot the graph: [tex]y=\dfrac{1}{x}[/tex]

Shift it 3 units left and 2 units down.

f(x + n) - shift n units left

f(x - n) - shift n units right

f(x) + n - shift n units up

f(x) - n - shift n units down

[tex]What graph represents the function f(x)=1/x+3-2[/tex]

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.