Range of a function using graph If we are given a function 
$$y = \frac{x-1}{x+2}$$
and we have to find the range . 
So I tried, I wrote
$$y = 1 - \frac3{x+2}$$
$$y-1 = \frac{-3}{x-2}$$
We know this is an equation of rectangular hyperbola , but 
how can I find range using its graph?
 A: Hint. Try taking the limits at $-\infty,~+\infty$ and also the right and left limits at $x_0=-2.$ You can verify that the range is $\mathbb{R}\setminus \{1\}$.
A: As an appendix to Nikolaos Skout's hint, the function looks like below. You should be able to imagine something like this using the usual methods and tricks in calculus for graphing functions.

A: The function $f(x) = 1/x$ has domain $D_f = (-\infty, 0) \cup (0, \infty)$ and range $R_f = (-\infty, 0) \cup (0, \infty)$.  

Based on your work, we can see that the graph of the function 
$$g(x) = \frac{x - 1}{x + 2} = 1 - \frac{3}{x + 2}$$
is obtained from the graph of $f(x)$ by reflecting the graph of $f(x)$ in the $x$-axis, stretching it vertically by a factor of $3$, and translating it two units to the left and one unit up.  Consequently, the domain of $g(x)$ is $D_g = (-\infty, -2) \cup (-2, \infty)$ and its range is $R_g = (-\infty, 1) \cup (1, \infty)$.

A: If you can graph it, you can determine its asymptotes. The range will be the set of y values that the curve sweeps over.
A: At $y = 1 - somehyperbola$ you're almost done.
The hyperbola can become anything except $0$. Add or subtract from $1$, you can have anything except $1$.
