# graph question...

• Jan 8th 2009, 02:26 PM
coyoteflare
graph question...
...

sorry about the lack of a graph shown

fig 10. shows a sketch of the graph $y=\frac{1}{x}$

i) sketch the graph $y=\frac{1}{x-2}$

ii) find the x-coordinates of the points of intersection of the graphs of $y=x$ and $y=\frac{1}{x-2}$

im not sure about the translation of this graph for question i.

question ii. i got as far as $(x-1)^2-1=1$

but then got $(x-1)^2=0$

which is wrong, can someone explain why $(x-1)^2=2$ is right?

also how would i position these points on sketch drawn in i. ?

thanks alot if you can help as this is the last bit of revision im doing for tomorrow!
• Jan 8th 2009, 02:44 PM
craig
1. You would transform this using the same rules as normal graphs, say for examply you have $y=x$ and $y=x-2$, whats translation would the second one be? Apply this rule to your graph, this is basic transformations.

2. At points of intersection the two graphs are equal, so we can say:

$x=\frac{1}{x-2}$, therefore $x(x-2)=1$.

$x^2 - 2x -1=0$. I am sure you can solve the resulting quadratic ;)

Hope this helps :)