Question

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

Answer 1

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)

$y=|x+4|$