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netineya [11]
2 years ago
13

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

Mathematics
1 answer:
tia_tia [17]2 years ago
8 0
<h2>Explanation:</h2><h2></h2>

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

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