Name: __________________________________________________________ Date: ____________________________
Families of Functions Worksheet
WARM UPS, Graphing Absolute Value with the Calculator
Graph the equation
on your graphing calculator:
Step 1: Hit the ‘y =’ button on the top left side of your calculator. Enter a negative (-) sign into the first Y =
Step 2: Hit the ‘MATH’ key
Step 3: Arrow over so the ‘NUM’ option is highlighted at the top of your screen
Step 4: Select option 1 – ‘1. abs(‘
Step 5: Enter the rest of your equation.
It should look like this:
Step 6: Graph the equation with a standard window
6
4
2
-5
CLASS NOTES, Vocabulary Words
Family of Functions:
Parent Function:
Transformation:
1. Translation:
2. Vertical Stretch:
3. Vertical Shrink:
4. Reflection:
Name: __________________________________________________________ Date: ____________________________
Exploring Families of Functions
Directions: Use your graphing calculator to graph the following equations and answer
the questions having to do with each graph.
Graph the parent equation
and sketch the graph:
A. Vertical Translation:
1. Graph the equation
on the same axis as the equation
. Describe what happened to
the parent function after the 3 was added. What is the vertex after the translation?
2. Graph the equation
on the same axis as the equation
What is the vertex after the translation?
3. Describe each translation of
a.
b.
and describe the translation.
without graphing. (Use the graph to check your answers):
Name: __________________________________________________________ Date: ____________________________
4. Write an equation for each translation of the parent function
graph be?
. What will the vertex of the new
a. Up 2 units
b. Down 8 units
B. Horizontal Translation:
1. Graph the equations
and
on the same set of axes. Describe what happens to the
parent function
when the 5 is subtracted from x on the inside of the absolute value sign. What
is the vertex after the translation?
2. Graph the equations
and
the vertex after the translation?
3. Describe each translation of
on the same set of axes. Describe the translation. What is
without graphing. (Check your answers):
a.
b.
4. Write an equation for each translation of the parent function
graph be after the translation?
a. Left 3 units
b. Right 7 units
C. Could Be Both!
. What will the vertex of the
Name: __________________________________________________________ Date: ____________________________
1. Describe each translation of
without graphing. (Check your answers):
a.
b.
c.
2. Write an equation for each translation of the parent function
after the translation?
. What is the vertex of the graph
a. Up 5 units, left 1 unit
b. Down 2 units, right 0.5 units
c. Down 7 units, left 9 units
D. Vertical Stretch/Vertical Shrink:
1. Graph
and
on the same set of axes. Describe what happens to the parent function
when the absolute value of x is multiplied by a factor of 2.
(**NOTE: each of the y-values in the function
2. Graph
and
is twice the corresponding value in
)
on the same set of axes and describe the transformation.
3. Graph
and
on the same set of axes and describe the transformation. Why do you
think this result is different than the results in questions D1 and D2?
Name: __________________________________________________________ Date: ____________________________
4. Graph
and
on the same set of axes. Describe the transformation.
5. Describe each transformation of the parent function
without graphing. (Check your answers):
a.
b.
6. Write an equation for each transformation of
:
a. Vertical stretch by a factor of 5
b. Vertical shrink by a factor of
c. Vertical stretch by a factor of 6
E. Reflection Across the x-axis:
(Hint: Imagine that the x-axis is a mirror!)
1. Graph
and
on the same set of axis. Describe what happens when a negative sign was
placed in front of the absolute value of x.
Name: __________________________________________________________ Date: ____________________________
2. Graph
and
on the same set of axis. Describe the transformation.
3. Which equation describes this graph?
a.
b.
c.
d.
4. A function is a vertical stretch of
function across the x-axis.
by a factor of 5. Write an equation for the reflection of the
F. Extension:
1. Patterns are used around us EVERYWHERE: quilts, wallpaper, tile floors, etc. The following pictures are
examples of certain types of patterns called Tessellations. State which kind of transformation(s) were
used to create each pattern.
Name: __________________________________________________________ Date: ____________________________
Homework #9 (due Wednesday):
Pg 97 #3-6, 12, 13, 17, 20, 29, 30, 35, 36, 44, 45