Explanation:
Here we have the following rational function:
[tex]f(x) = \frac{1}{x+3} -2[/tex]
So the graph of this function is shown in the First Figure below. Let's define another function which is a parent function:
[tex]g(x)=\frac{1}{x}[/tex]
Whose graph is shown in the second figure below. So we can get the graph of f from the graph of g this way:
Step 1. Shift the graph 3 units to the left:
[tex]f_{1}(x) = \frac{1}{x+3}[/tex]
Step 2. Shift the graph 2 units down:
[tex]f(x) = \frac{1}{x+3}-2[/tex]
Finally, the features of the graph of f are:
The graph of this function comes from the parent function g and the transformations are:
- A shifting 3 units to the left
