Question 22362
not quite sure what you are asking here. I think you are asking for your answers to be checked?


f(x) is re-written as {{{((x+3)(x-4))/(x-2)}}}, correct.


So, domain. This is ONLY asking you, what values of x can you put in to this equation? To answer this, it is easier to ask yourself, which x-values can i NOT put into the equation? That answer is x=+2, since this value, makes the denominator zero and then the function goes haywire there!.

So, the domain is ANY VALUE OF x, but not +2.

This is written as xeR, x /= +2 (i cannot write the correct symbols here: /= is supposed to be an equals with a diagonal line through it)
 

Zeroes? These are the roots of the equation. where does it cross the x-axis. The answer is at points x=-3 and x=4.


The graph is:

{{{graph(200,200,-5,5,-10,10, ((x+3)(x-4))/(x-2))}}}


but note that the vertical line at x=2 is NOT part of the graph. The graph is 2 separate curves that head towards but never quite reach the x=2 vertical...this is called the asymptote.


Hope this helps


jon.