Question 82619
 In order to graph {{{1/(x-2)}}}, we need to plot some points. 
 So we can start at any x value. So lets start at x=-5 
 

{{{y=1/(x-2)}}} Start with the given equation 
 
{{{y=1/((-5)-2)}}} Plug in {{{x=-5}}} 
 
{{{1/((-5)-2)=-0.142857142857143}}} Calculate the y value

So when {{{x=-5}}} {{{y=-0.142857142857143}}}

So our 1st point is (-5,-0.142857142857143)




 

{{{y=1/(x-2)}}} Start with the given equation 
 
{{{y=1/((-4)-2)}}} Plug in {{{x=-4}}} 
 
{{{1/((-4)-2)=-0.166666666666667}}} Calculate the y value

So when {{{x=-4}}} {{{y=-0.166666666666667}}}

So our 2nd point is (-4,-0.166666666666667)




 

{{{y=1/(x-2)}}} Start with the given equation 
 
{{{y=1/((-3)-2)}}} Plug in {{{x=-3}}} 
 
{{{1/((-3)-2)=-0.2}}} Calculate the y value

So when {{{x=-3}}} {{{y=-0.2}}}

So our 3rd point is (-3,-0.2)




 

{{{y=1/(x-2)}}} Start with the given equation 
 
{{{y=1/((-2)-2)}}} Plug in {{{x=-2}}} 
 
{{{1/((-2)-2)=-0.25}}} Calculate the y value

So when {{{x=-2}}} {{{y=-0.25}}}

So our 4th point is (-2,-0.25)




 

{{{y=1/(x-2)}}} Start with the given equation 
 
{{{y=1/((-1)-2)}}} Plug in {{{x=-1}}} 
 
{{{1/((-1)-2)=-0.333333333333333}}} Calculate the y value

So when {{{x=-1}}} {{{y=-0.333333333333333}}}

So our 5th point is (-1,-0.333333333333333)




 

{{{y=1/(x-2)}}} Start with the given equation 
 
{{{y=1/((0)-2)}}} Plug in {{{x=0}}} 
 
{{{1/((0)-2)=-0.5}}} Calculate the y value

So when {{{x=0}}} {{{y=-0.5}}}

So our 6th point is (0,-0.5)




 

{{{y=1/(x-2)}}} Start with the given equation 
 
{{{y=1/((1)-2)}}} Plug in {{{x=1}}} 
 
{{{1/((1)-2)=-1}}} Calculate the y value

So when {{{x=1}}} {{{y=-1}}}

So our 7th point is (1,-1)




 

{{{y=1/(x-2)}}} Start with the given equation 
 
{{{y=1/(x-2)=1/0}}} Plug in {{{x=2}}} 
 
Since we cannot divide by zero, the y value is undefined 
 
 
 
 
{{{y=1/(x-2)}}} Start with the given equation 
 
{{{y=1/((3)-2)}}} Plug in {{{x=3}}} 
 
{{{1/((3)-2)=1}}} Calculate the y value

So when {{{x=3}}} {{{y=1}}}

So our 9th point is (3,1)




 

{{{y=1/(x-2)}}} Start with the given equation 
 
{{{y=1/((4)-2)}}} Plug in {{{x=4}}} 
 
{{{1/((4)-2)=0.5}}} Calculate the y value

So when {{{x=4}}} {{{y=0.5}}}

So our 10th point is (4,0.5)




 

{{{y=1/(x-2)}}} Start with the given equation 
 
{{{y=1/((5)-2)}}} Plug in {{{x=5}}} 
 
{{{1/((5)-2)=0.333333333333333}}} Calculate the y value

So when {{{x=5}}} {{{y=0.333333333333333}}}

So our 11th point is (5,0.333333333333333)




 



Now lets make a table of the values we have calculated

<pre>
<TABLE width=500>

<TR><TD> x</TD><TD>y</TD></TR>

<TR><TD> -5</TD><TD>-0.142857142857143</TD></TR> 
<TR><TD> -4</TD><TD>-0.166666666666667</TD></TR> 
<TR><TD> -3</TD><TD>-0.2</TD></TR> 
<TR><TD> -2</TD><TD>-0.25</TD></TR> 
<TR><TD> -1</TD><TD>-0.333333333333333</TD></TR> 
<TR><TD> 0</TD><TD>-0.5</TD></TR> 
<TR><TD> 1</TD><TD>-1</TD></TR> 
<TR><TD> 2</TD><TD>Undefined</TD></TR> 
<TR><TD> 3</TD><TD>1</TD></TR> 
<TR><TD> 4</TD><TD>0.5</TD></TR> 
<TR><TD> 5</TD><TD>0.333333333333333</TD></TR> 
</TABLE>
</pre>Now plot the points

{{{drawing( 900, 900, -10, 10, -10, 10,
  grid( 1 ),circle(-5,-0.142857142857143,0.05), 
  circle(-5,-0.142857142857143,0.08), 
circle(-4,-0.166666666666667,0.05), 
  circle(-4,-0.166666666666667,0.08), 
circle(-3,-0.2,0.05), 
  circle(-3,-0.2,0.08), 
circle(-2,-0.25,0.05), 
  circle(-2,-0.25,0.08), 
circle(-1,-0.333333333333333,0.05), 
  circle(-1,-0.333333333333333,0.08), 
circle(0,-0.5,0.05), 
  circle(0,-0.5,0.08), 
circle(1,-1,0.05), 
  circle(1,-1,0.08), 
circle(3,1,0.05), 
  circle(3,1,0.08), 
circle(4,0.5,0.05), 
  circle(4,0.5,0.08), 
circle(5,0.333333333333333,0.05), 
  circle(5,0.333333333333333,0.08) 
)}}}

Now connect the points, this is the graph of {{{1/(x-2)}}}

{{{drawing( 900, 900, -10, 10, -10, 10,
  grid( 1 ),
  graph( 900, 900,-10, 10, -10, 10, 1/(x-2)),circle(-5,-0.142857142857143,0.05), 
  circle(-5,-0.142857142857143,0.08), 
circle(-4,-0.166666666666667,0.05), 
  circle(-4,-0.166666666666667,0.08), 
circle(-3,-0.2,0.05), 
  circle(-3,-0.2,0.08), 
circle(-2,-0.25,0.05), 
  circle(-2,-0.25,0.08), 
circle(-1,-0.333333333333333,0.05), 
  circle(-1,-0.333333333333333,0.08), 
circle(0,-0.5,0.05), 
  circle(0,-0.5,0.08), 
circle(1,-1,0.05), 
  circle(1,-1,0.08), 
circle(3,1,0.05), 
  circle(3,1,0.08), 
circle(4,0.5,0.05), 
  circle(4,0.5,0.08), 
circle(5,0.333333333333333,0.05), 
  circle(5,0.333333333333333,0.08) 
)}}}