Describe the parent function and then use a table of values to graph the functions.
Graph:
Transformation: A horizontal translation 5 units right.
Practice makes perfect
The given function is an absolute value function, so its parent function is f(x)=|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
f(x)=|x|
g(x)=|x-5|
-2
|-2|= 2
|-2-5|= 7
0
|0|= 0
|0-5|= 5
5
|5|= 5
|5-5|= 0
7
|7|= 7
|7-5|= 2
Now let's plot the functions using these points! Remember that the graph of absolute value functions is V-shaped.
Comparing the Functions
Having drawn our functions, we can describe the transformation.
We see that each y-value is being shifted 5 units to the right. This is a horizontal translation.
