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Describe the parent function and then use a table of values to graph the functions.
Graph:
Transformation: A vertical translation 4 units up.
The given function is an absolute value function, so its parent function is y=|x|. We will start by graphing both functions in one coordinate plan. Then we will compare them to describe the transformation.
To graph both of the functions we will use a table of values. We will choose a variety of x-values: at least one negative, 0, and at least one positive.
x | y=|x| | f(x)=4+|x| |
---|---|---|
-2 | |-2|= 2 | 4+|-2|= 6 |
0 | |0|= 0 | 4+|0|= 4 |
2 | |2|= 2 | 4+|2|= 6 |
Now let's plot the functions using these points! Remember that the graphs of absolute value functions are V-shaped.
Having drawn our functions, we can describe the transformation.
We see that each y-value is being shifted 4 units up. This is a vertical translation.