Name:_________________________________________ Per:______
Project: Absolutely Understanding Absolute Value Graphs
A2.A.46- Perform transformations with functions and relations: f(x + a), f(x) + a, f(-x), -f(x), af(x)
Activity:
In each section, you will graph the absolute value function using a table of values.
11.17.11
Part I :
In this activity, you will explore the similarities and differences between the parent absolute value function (the
motherfunction!) and other absolute value functions. On the graph, plot the points for the function y = |x|. You will need
to show your calculations and table of values. Once you have created a set of ordered pairs and correctly placed them on
the coordinate plane, and connect the points.
Make note of the distinctive features of the absolute value graph: _______________________________________
Part II:
1. On the next graph, plot the points for the function, y = |x| + 2. Again, you will need to show your calculations and table
of values. Once you have generated these ordered pairs and plotted them on the coordinate plane, examine the graphs and
begin to make some mental observations about these two functions. What is different about these two functions?
Mathematically describe the difference between this function and the function from Part 1.
2. On the next coordinate plane, plot and graph y = |x| – 5. How does this graph differ from the parent function? How
does the graph differ from the one you graphed in #1?
3. Can you predict what a graph of y = |x| + 7 look like? Describe it below. How will it differ from the parent function?
Part III:
1. On the next graph, plot the points for the function, y = |x + 2|. You need to show your calculations and table of values.
How does this absolute value graph differ from the parent function? Describe the placement of the graph.
2. Graph of y = |x – 6| + 1. Show your calculations and your table of values.
Describe the placement of the graph. How does this compare to the parent function?
3. Could you predict what the graph of y = |x + 4| will look like? Describe the graph in comparison with the parent
function.
4. Could you predict what the graph of y = |x - 2| -4 will look like? Describe the graph in comparison with the parent
function.
Part IV:
1. On the next graph, plot the points for the function, y = -|x|. You need to show your calculations and a table of values.
How does this absolute value graph differ from the parent function? Describe the graph.
Part V:
1. On the next graph, plot the points for the function, y = 2|x|. You need to show your calculations and a table of values.
Describe the graph. How does this absolute value graph differ from the parent function?
2. On the next graph, plot the points for the function, y 
x
2
How does this absolute value graph differ from the parent function? Describe the graph.
FOLLOW UP QUESTIONS: After completing the above activity, you should be able to describe the functions below
without EVER using your calculator. Describe the transformations of these functions. Say if the function will shift left or
right, up or down, get more narrow or fatter, or flip upside-down.
1. y = |x + 4| ___________________________________________________________________________________
____________________________________________________________________________________
2. y = -|x| + 4___________________________________________________________________________________
____________________________________________________________________________________
3. y = 3|x| ___________________________________________________________________________________
____________________________________________________________________________________
4. y = |x – 4| - 3 ___________________________________________________________________________________
____________________________________________________________________________________
5. y = -2|x| ___________________________________________________________________________________
____________________________________________________________________________________
6. y = |x| + 6___________________________________________________________________________________
____________________________________________________________________________________
7. y 
x
4
 1 ___________________________________________________________________________________
____________________________________________________________________________________
8. y = 2|x + 4| – 6 ___________________________________________________________________________________
____________________________________________________________________________________
9. In the equation y = a|x - h| + k, explain how each letter affects (changes) the graph of the parent function y = |x|
a –_______________________________________________________________________________
h – ______________________________________________________________________________
k – _______________________________________________________________________________