# How do you graph # f(x)= x/(x+3)#?

##### 1 Answer

graph{1-3/(x+3) [-10, 10, -15, 15]}

#### Explanation:

First of all, we see that the function is not defined at

More than that, as

If

Continuing analysis, we can see that, as

Now about constructing a graph.

The easiest way is to transform our function as follows:

So, we have to graph

According to the rules of graph transformation (seeUnizor - *Algebra* - *Graph*) we can construct this graph in the following steps:

Step 1. Graph

graph{1/x [-10, 10, -15, 15]}

Step 2. Shift it to the left by

graph{1/(x+3) [-10, 10, -15, 15]}

Step 3. Stretch it vertically by a factor of

graph{3/(x+3) [-10, 10, -15, 15]}

Step 4. Invert the graph (positive - to negative, negative - to positive), thus getting the graph of

graph{-3/(x+3) [-10, 10, -15, 15]}

Step 5. Finally, shift the graph up by

graph{1-3/(x+3) [-10, 10, -15, 15]}