# Range of a function

1. Oct 7, 2007

### CathyLou

Hi.

Could someone please tell me the Core 3 way of finding the range of f(x) = (2x - 3) / (x - 2).

I have no idea how to draw the graph.

Any help would be really appreciated.

Thank you.

Cathy

2. Oct 7, 2007

### arildno

Well, you know that x can't be 2, right?

Now, let "t" denote some arbitrary real number; we are to find out what x must be in order for f to eqal f:
$$t=\frac{2x-3}{x-2}\to(x-2)t=2x-3\to{x}=\frac{2t-3}{t-2}, x\neq{2}$$
Thus, t=2 is an inadmissible value for the function.

Note that t=2 is a horizontal ASYMPTOTE for f(x) as x trundles off to either infinity.

Furthermore, there are no t-value such that $$\frac{2t-3}{t-2}=2$$, whereupon we have shown that the range of f is all real numbers except 2.

Last edited: Oct 7, 2007