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Describing Transformations of Rational Functions

Describing Transformations of Rational Functions 1.9 - Solution

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Let's start by recalling possible transformations of the parent function

Function Transformation of the Graph of
Horizontal translation by units.
If the translation is to the right.
If the translation is to the left.
Vertical translation by units.
If the translation is up.
If the translation is down.
Vertical stretch or shrink by a factor of
If it is a vertical stretch.
If it is a vertical shrink.

Now, let's consider the given function. We can see that and From here, we can determine the transformations.

  1. A vertical stretch by a factor of
  2. A horizontal translation unit to the left.
  3. A vertical translation units down.

Using these transformations, we can find the asymptotes and the reference points of the graph of Note that the horizontal translation affects only the coordinates, while the vertical stretch and vertical translation affect only the coordinates.

Object
Vertical asymptote

Horizontal asymptote

Reference point

Reference point

Next, we will use the table above to graph and