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.
Graphing the Functions
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.
Comparing the Functions
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.
