Audience
 Class of 26 10th and 11th grade regular
education students
 2 students are resource and need extended
time.
 All students have experience with inspiration
and Microsoft Word.
Family of Functions
OBJECTIVES
Algebra
Grade 9
13. Translate between the characteristics defining a line (i.e., slope,
intercepts, points) and both its equation and graph (A-2-H) (G-3H)
15. Translate among tabular, graphical, and algebraic
representations of functions and real-life situations (A-3-H) (P-1H) (P-2-H)
Grade 11/12
4. Translate and show the relationships among non-linear graphs,
related tables of values, and algebraic symbolic representations
(A-1-H)
Objectives
8. Categorize non-linear graphs and their equations as quadratic,
cubic, exponential, logarithmic, step function, rational,
trigonometric, or absolute value
(A-3-H) (P-5-H)
Geometry
Grade 9
26. Perform translations and line reflections on the coordinate
plane (G-3-H)
Grade 11/12
16. Represent translations, reflections, rotations, and dilations of
plane figures using sketches, coordinates, vectors, and matrices
(G-3-H)
Objectives
Patterns, Relations, and Functions
Grade 9
40. Explain how the graph of a linear function changes as the
coefficients or constants are changed in the function’s symbolic
representation (P-4-H)
Grade 11/12
25. Apply the concept of a function and function notation to
represent and evaluate functions (P-1-H) (P-5-H)
29. Determine the family or families of functions that can be used to
represent a given set of real-life data, with and without
technology (P-5-H)
Objectives
Use Inspiration to state properties of the family
of functions
Use Microsoft Word to write a story to
demonstrate the properties of a v shaped
animal
Use a graphing calculator to examine the following
functions then use Microsoft Word to write a short
description of what you observed.
1. y = x
2. y = |x|
3. y = x2
Graphing y = x
“Turn your calculators on.”
“Press on the Y= key.”
“Press on the x key”
(Note: that it is diagonal to the 2nd function key)
“Press on the Graph key.”
Students should see the following graph on their
calculator:
Family of Functions
TYPE
FUNCTION
SHAPE OF GRAPH
LINEAR
f(X) = x
ABSOLUTE
VALUE
f(x) = |x|
V
QUADRATIC
f(X) = x2
U
For each function, state the type of
function and the shape of the graph
1.
2.
3.
4.
5.
6.
7.
8.
f(x) = 3(x + 4) – 5
g(x) = -2|x + 4| + 7
h(x) = 1/5(x – 0) + 0
f(x) = 1/5(x - 10)2 – 4
f(x) = 3x2 + 9
g(x) = |x| + 7
h(x) = x + 4
f(x) = 5(x - 3)2
1.
2.
3.
4.
5.
6.
7.
8.
Linear, line
Absolute value, V
Linear, line
Quadratic, U
Quadratic, U
Absolute value, V
Linear, line
Quadratic, U
Translating
Linear Functions
Use a graphing calculator to examine the following
functions then use Microsoft Word to write a short
description of what you observed.
1. f(x) = x + 4
2. f(x) = x – 6
3. f(x) = -x + 8
4. F(x) = ½x - 1
Use inspiration to create a bubble
map to describe what could happen
to a linear function.
Translation
 Moving a graph from one location to another
without changing the shape or size
 Graphs can be moved left, right, up, down, or
in combinations of up and right etc.
Translating Linear Functions
parent function
Can be changed to
 f(x) = x
 f(x) = a(x + h) + k
 f(x) = a(x – h) + k
 f(x) = a(x + h) – k
 f(x) = a(x – h) - k
What happens to the graph f(x) = x
When a number is
added to x?
2. When a number is
subtracted from x?
3. When a number is
added to k?
4. When a number is
subtracted from k?
1.
Moves graph to the
left
2. Moves graph to the
right
3. Moves graph up
4. Moves graph down
1.
What happens to the graph f(x) = x
5. When f(x) is multiplied
by a number between
0 and 1
6. When f(x) is multiplied
by a number greater
than 1
7. When f(x) is opposite
5. The line is not as steep
6. The line is steeper
7. The lines changes
directions
Speed Graphing
 Write the translation as an ordered pair
 Plot the translation
 Write the slope as a fraction
 Plot the slope from the translation point let the
numerator be y and the denominator be x
 Draw your line
Speed Graph and describe what
happens with the following
f(x) = 3(x + 4) – 5
2. g(x) = -2(x + 4) + 7
3. h(x) = 1/5(x – 0) + 0
4. f(x) = 1/5(x -10) - 4
1.
Use Microsoft Word to write an equation and draw
an example to represent each of the 3 family of
functions.
Call on several students to share work with the class
Translating absolute
Value Functions and
Parabolas
Can Absolute value functions and
quadratics be translated?
Yes, they can be
translated just like
linear functions
General Form of Functions
Type
General Form
Example
Linear
f(x) = a(x - h) + k
f(x) = 2(x - 3) + 5
Absolute value
f(x) = a|x – h| + k
f(x) = ½|x + 6| + 9
Parabola
f(x) = a(x - h)2 + k f(x) = -3(x - h)2 - 7
a, h and k are any real number
Have students work in pairs to use
write and draw 5 equations for
absolute value functions and
quadratics to show them translated in
different positions. Have each group
share with the class.
Saga of a V Shaped Animal
You are an animal of your choice, real or make-believe, in the
shape of an absolute value function. Your owner is an Algebra II
student who moves you, stretches you, hugs you, and turns you
upside down. Using all you know about yourself and Microsoft
Word, describe what is happening to you while the Algebra II
student is playing with you. You must include at least ten facts or
properties of the Absolute Value Function, f(x) = a|x – h| + k in your
story. Discuss all the changes in your shape as a, h, and k change
from positive, negative, or zero and get smaller and larger. Discuss
the vertex, the equation of the axis of symmetry, whether you open
up or down, how to find the slope of the two lines that make your
“Vshape,” and your domain and range. (Write a small number
(e.g., 1, 2, etc.) next to each property in the story to make sure you
have covered ten properties
A sample story would go like this:
“I am a beautiful black and gold Monarch butterfly named Abby flying
around the bedroom of a young girl in Algebra II named Sue. Sue
lies in bed and sees me light on the corner of her window sill, so my
(h, k) must be (0, 0) 1. I look like a “V” 2 with my vertex at my head
and wings pointing at the ceiling at a 45 angle 3. My “a” must be
positive one 4. I am trying to soak up the warm rays of the sun so I
spread my wings making my “a” less than one 5. The sun seems to
be coming in better in the middle of the window sill, so I carefully
move three hops to my left so my “h” equals 3 6. My new equation
is now y = .5|x + 3| 7. Sue decided to try to catch me, so I close my
wings making my “a” greater than one 8. I begin to fly straight up
five inches making my “k” positive five 9 and my new equation y =
2|x + 3| + 5 10. Then I turned upside down trying to escape her
making my “a” negative 11. Sue finally decided to just watch me and
enjoy my beauty. ”
Rubric for project
2 pts.
-Answers in paragraph form
In complete sentences with
proper grammar and
punctuation
2 pts.
-Correct use of mathematical
language
2 pts.
-Correct use of mathematical
symbols
3 pts/discussion -each property used correctly