Pearson Algebra 2 Common Core, 2011
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Pearson Algebra 2 Common Core, 2011 View details
Mid-Chapter Quiz
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Exercise 12 Page 526

Start by recalling the translations of the parent function,

The graph of is the graph of translated units to the left and units down.

Practice makes perfect
We want to explain the relation between the given two functions.
Notice that is the transformation of To define this transformation, we will recall the possible translations.
Translations of
Vertical Translations
Horizontal Translations

Using this table, let's indicate the translation from the graph of the parent function to the graph of and

Function Translation
Translation up units and right unit
Translation down units and left unit

Let's draw the graphs of these two functions on the coordinate plane.

translations of the parent function

Finally, let's consider a point on the graph of We will see the translation applied to obtain its corresponding point on the graph of For simplicity, let's use the point

corresponding points

Therefore, the graph of is the graph of translated units to the left and units down.