Big Ideas Math Algebra 1, 2015
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Big Ideas Math Algebra 1, 2015 View details
7. Graphing Absolute Value Functions
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Exercise 34 Page 161

First we will go through all the transformations from the graph of to the graph of given function. After that we will make a table of values to graph this function.

Transformations

The given equation is a transformation of the parent function We can define each transformation from the inside to the outside. We will start with the transformation closest to and end with the farthest from Let's review our function.
First, there is a horizontal translation units to the left, Remember, typically is a horizontal translation units to the right, while is translated units to the left.

Next, we have a vertical translation units up, Remember, in most cases is a vertical translation units up, while is translated units down.

Graphing

To graph the function without going through the entire process of transforming the parent function, we could instead make a table of values. Then we only need to plot the ordered pairs that we find.

Simplify

Now we can plot these points and connect them to create our graph of