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 62 Page 162

Recall the general forms for translations.

Is Our Friend Correct? No
Explanation: See solution.

Practice makes perfect
Let's start by recalling the general forms for horizontal and vertical translations of an absolute value function.
When considering a horizontal translation, we subtract the number of units that we are translating a graph. Since can be written as and we know that is a positive number, the graph of represents a horizontal translation of the graph of in the negative direction. Let's make a table of values for

Let's now make a table of values for We will arbitrarily let resulting in the function

Finally let's make a table for with The resulting function is

We can plot and connect the obtained points in the same coordinate plane. Keep in mind that the graph of an absolute value function has a V shape.

Though it may seem counterintuitive, the graph of is a negative horizontal translation of the graph of by units. Conversely, the graph of is a positive horizontal translation of the graph of by units.