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 7 Page 159

Practice makes perfect
a We are given the following absolute value equation.
This is a transformation of the parent function To see how each of the parameters is affecting the parent function, it will be helpful to rewrite it first.
This way we can look at each of the transformations individually. Notice that there is no general recipe for how to obtain a function from its parent function by transformations. However, there are a couple good things to remember.
  • Usually, we want to look at horizontal transformations before any vertical transformations.
  • Begin with the reflections.

First, we can do a reflection in the axis. This will transform the graph of the parent function, to the graph of Notice that, since the graph of is symmetrical about axis, this will not change how it looks.

Now, let's do a horizontal translation units to the right. Then the graph of becomes

Next, we will do a vertical shrink by a factor of This transforms the graph of to the graph of

Finally, we have a vertical translation unit up. From we get the final graph,

Notice that there are many ways to obtain the graph of our function transforming the graph of its parent function. Here we considered only one of the many possibilities.

b To graph the function without going through the entire process of transforming the parent function, we can 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