did you notice that
f(x) = (x-9)(x-2)/(x-9) ??
= x-2, x ≠ 9
So for all values of x except x=9
the given function reduces to
f(x) = x-2
which is a straight line.
when x = 9, the original gives you 0/0 which is indeterminate, while the reduced function gives you
(9,7)
So the graph would be the straight line
y = x-2, with a hole at (9,7)
try this:
let x = 8.999 and sub into the original using your calculator, you should get 6.999
let x = 9.00001 in the original
you will get 7.00001
which of course you will get in that exact form if you use y = x-2
However, when you use to calculator to find
f(9) using the original you will get an error , while
f(9) in the simplified version will give you 7
The graph of f(x)= (x^2 - 11x + 18)/(x-9) consists of a line and a hole. Find the equation of the line and the coordinates of the hole.
I really have no idea how to do this. I tried factoring it and ended up with (x-2), but I don't know how that helps me. please help
2 answers
Wow, I didn't realize that finding (x-2) was already finding the equation of the line. Thanks!