Question

Analyze the key features of the graph f(x) = 1/x+3 -2

Answer 1

Explanation:

Here we have the following rational function:

$f(x) = \frac{1}{x+3} -2$

So the graph of this function is shown in the First Figure below. Let's define another function which is a parent function:

$g(x)=\frac{1}{x}$

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:

$f_{1}(x) = \frac{1}{x+3}$

Step 2. Shift the graph 2 units down:

$f(x) = \frac{1}{x+3}-2$

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

• A shifting 2 units down