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

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

## This Post Has 8 Comments

1. lkarroum3733 says:

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

2. jerali says:

The graph as shown below.

Step-by-step explanation:

Given : The function $f(x)=\frac{1}{x-3}-2$

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

Consider the given function $f(x)=\frac{1}{x-3}-2$

Domain of function $f(x)=\frac{1}{x-3}-2$

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 $x<3\quad \mathrm{or}\quad \:x3$

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

Inverse of given function is  $y=\frac{3x+7}{x+2}$

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

Now, x intercept and y- intercepts

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

Let f(x) = y

Then $y=\frac{1}{x-3}-2$

Put x = 0

thus y- intercept is $\left(0,\:-\frac{7}{3}\right)$

Now put y = 0

Then  x- intercept is $\left(\frac{7}{2},\:0\right)$

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.

$\lim _{x\to a^-}f\left(x\right)=\pm \infty$

$\lim _{x\to a^+}f\left(x\right)=\pm \infty$

Thus, The vertical asymptotes is x = 3

And For horizontal asymptotes,

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

We have y = -2 as horizontal asymptotes.

Plot we get the graph as shown below.

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

3. LucindaKamala says:

files are attached below

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

4. Lucki1944 says:

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

The equation is:

f(x) = 1/x - 1

Domain

All real numbers except for {0}

$Which graph represents the function f(x) = 1/x - 1?$

5. hayleegreenwell34 says:

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.

6. angelaisthebest1700 says:

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.

7. haileysolis5 says:

Plot the graph: $y=\dfrac{1}{x}$

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

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

8. tifftifftiff5069 says:

Figure 2

Step-by-step explanation:

We are given the function $f(x)=\frac{1}{x-1}$.

Now, when x = 1, we have that,

$f(x)=\frac{1}{1-1}$ i.e. $f(x)=\frac{1}{0}$ i.e. $f(x)\rightarrow\infty$.

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

$f(x)=\frac{1}{-1-1}$ i.e. $f(x)=\frac{1}{-2}$.

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

$-1=\frac{1}{x-1}$ i.e. $-x+1=1$ i.e. $x=0$.

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

Hence, figure 2 is the correct option.