Big Ideas Math Algebra 1, 2015
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Big Ideas Math Algebra 1, 2015 View details
1. Graphing Square Root Functions
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Exercise 10 Page 546

Consider vertical and horizontal translations, stretches and shrinks, and reflections.

Transformation: A horizontal translation left units followed by a vertical shrink by a factor of and a vertical translation up unit.
Graph:

Practice makes perfect

We want to describe the transformations of the parent function represented by

Identifying the Transformations

Let's look at the possible transformations. Then we can more clearly identify the ones being applied.

Transformations of
Vertical Translations
Vertical Stretch or Shrink
Horizontal Translations
Now, using the table, let's highlight the transformations.
We can describe the transformations as a horizontal translation left units followed by a vertical shrink by a factor of and a vertical translation up unit. We will consider those transformations one at the time.

Horizontal Translation

Let's consider the first transformation being applied to the parent function, a horizontal translation left units. Applying this transformation to the graph of will result in the graph of
Now, we can apply this transformation and obtain the graph of

Vertical Shrink

Now, let's consider the second transformation, a vertical shrink by a factor of Applying this transformation to the graph of will result in the graph of
Now, we can apply this transformation and obtain the graph of

Vertical Translation

Let's consider the last transformation, a vertical translation up unit. Applying this transformation to the graph of will result in the graph of
Finally, we can apply this transformation and obtain the graph of