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Practice: Writing equations of an absolute value finction from its graph.Write an equation for each translation of y=|x| shown below

Practice: Writing equations of an absolute value finction from its graph.Write an-example-1
User Rahulm
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1 Answer

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According to the information given, each graph shows a translation of this Absolute Value Function:


y=|x|

Then, you need to remember the following Transformation Rules for Functions:

1. If:


f(x)-k

The function is translated down "k" units.

2. If:


f(x)+k

The function is translated up "k" units.

3. If:


f(x-h)

The function is translated right "h" units.

4. If:


f(x+h)

The function is translated left "h" units.

By definition, the Parent Function of an Absolute Value Parent Function is:


y=|x|

And its vertex is at the Origin.

Then, you can identify that:

a) The graph that is given in "Part a" shows that the Parent Function was translated down 3 units. Then, the new equation for the function is:


y=|x|-3

b) Notice that the graph that is given in "Part b", shows that the Parent Function was translated 1 unit up. Then, the new equation for the function is:


y=|x|+1

c) For this part, you can identify that the Parent Function was translated 1 unit to the right. So the equation is:


y=|x-1|

d) The graph shows that the Parent Function was translated 4 units to the left. Then, you can set up this equation:


y=|x+4|

Therefore, the answers are:

a)


y=|x|-3

b)


y=|x|+1

c)


y=|x-1|

d)


y=|x+4|

User Dzamo Norton
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