Alg2X – UNIT 2
Alg2X – UNIT 2
Name__________________________________________
Period__________
If the directions state to EXPLAIN you need to string words
together to form a sentence. Deductions for not following
directions.
DAY
TOPIC
ASSIGNMENT
1
Domain, Range, Relations vs. Functions, Vertical Line Test (p.
48 #21, 31-37 if time)
1.6 pp. 47-48 #1-29 ODD, 31-33 (skip 5,11,21) 44, 46
2
Function notation, independent/dependentVariables, Graphing
Functions, Word Problems
(p. 55 #21; if time go over graph for #s 33-37)
1.7 pp. 54-55 #1-37 odd (skip 11,19,21, 29, 31) 50-53
3
More of Days 1 and 2
WORKSHEETS in Packet
4
Review (10-15 min.)
QUIZ
TBD
5
Intro to 5 “Parent Functions” (Constant, Linear, Quadratic,
Cubic, Square Root) and their transformations (Using Graphing
Calculator)
1.9 pp.70-73 #1-7, 11, 12, 17-19 (use the table feature on calc
to help)
6
Compound Inequalities
2.8 pp.154-156 # 1-4, 14, 15, 28-36 (HW in PACKET)
7
Absolute Value Equations
2.8 pp.154-156 #5-7, 16-19, 38, 49
8
Absolute Value Inequalities
2.8 pp.154-156 #8-13, 36, 39, 41, 42, 55-58
9
Absolute Value Functions – Graphs, Translations, Reflections
2.9 pp.161-163 # 2-6, 19-24, 27-29, 33, 36
10
Review
pp. 78 #36-46, 53-54, p. 169 #47-56, 58
or a worksheet
11
More Review
And Word Problems
Worksheet
12
TEST
See page 31 of packet
Reminders:
Bring your calculator every day.
Missed Tests/Quizzes:
avoid 20% reduction; don’t forget. Manage your school work
please.
Mini Quizzes are always open-note.
Work hard but try not to stress.
Life REALLY is too short.
(2)_______
(0)_______
f
f
=
=
(2)_______
f
=
(3)_______
f
-=
A _____________________is a set of pairs of input and output
values. You can write them as ordered pairs.
The ___________________ of a relation is the set of all inputs,
or x-coordinates of the ordered pairs.
The ____________________ of a relation is the set of all
outputs, or y-coordinates of the ordered pairs.
A _______________________ is a relation in which each element of
the domain is paired with exactly one element in the range.
Look for: The same x-value, but different y-values! This means
it is not a function!
Are the following relations function? State why or why not! Then
state the domain and range!
a)
(
)
(
)
(
)
(
)
{
}
5,1,3,5,8,1,2,7,
--
b)
(
)
(
)
(
)
(
)
{
}
3,1,2,4,3,3,1,0,
-
Function: _________
Function: _________
Domain: __________________
Domain: __________________
Range: ___________________
Range: ___________________
Mapping Diagram: Identify the domain and range. Then tell
whether the relation is a function.
Input
Output
Input
Output
-3
3
-3
3
1
-2
1
1
4
1
3
4
4
-2
Function: _________
Function: _________
Domain: __________________
Domain: __________________
Range: ___________________
Range: ___________________
Vertical Line test: A relation is a function if and only if no
vertical line intersects the graph of the relation at more than one
point. If a vertical line passes through two or more points on the
graph, then the relations is not a function.
Using the Vertical Line Test, determine whether each relation is
a function. Then state the domain & range.
2
-2
fx = 3x+2
Function: _________
Function: _________
Function: _________
Domain: __________________Domain: __________________Domain:
__________________
Range: ___________________Range: ___________________Range:
___________________
Function: _________
Function: _________
Domain: __________________
Domain: __________________
Range: ___________________
Range: ___________________
For a graph to be a function, all vertical lines must touch in
only _____ spot (or not touch at all)
For the domain, scan your eyes from __________ to
___________.
For the range, scan your eyes from the ___________________ to
the ___________.
Earnings Per Hour
Name
Bob
Dave
Jane
Sam
Pay
$9
$11
$5
$15
Test Scores
Name
Jim
Greg
Jorge
Terrell
Score
65
91
94
88
Function: _________
Function: _________
Domain: __________________
Domain: __________________
Range: ___________________
Range: ___________________
Closure
Why is
(
)
(
)
{
}
2,1,3,1
a function, but
(
)
(
)
{
}
2,1,2,3
is not?
Function Notation:
32
yx
=+
can be written in a “fancy notation” (
(
)
32
fxx
=+
.
(
)
fx
is read as _________________________ and does NOT mean f times
x.
“Normal Way”
Function Way
(
)
1,5
(
)
15
f
=
Simplify
21
yx
=-
when
3
x
=
(
)
21
fxx
=-
; find
(
)
3
f
Given
(
)
32
fxx
=-
and
2
()3
gxx
=+
, find the following:
a)
(2)
f
b)
(3)
g
-
c)
(4)
f
d)
(5)
g
e)
1
()
2
f
f) *
((3))
gf
Find
(1), (2), (0)
fff
-
.
Find
(1),(3), g(5)
gg
-
.
Graphing functions: Do this the same why we learned to graph
lines, but just replace the
()
fx
(or whatever letter it is) with ______!
Example:
()21
fxx
=-
Example 2:
()
gxx
=
Example 3:
()1
hxx
=+
Word Problems: FUN FUN FUN!
2
-2
Directions: Explain a possible domain and range for each
situation
4
2
fx = x
2
8
6
4
2
-2
-4
-6
-8
-55
10
5
-5
10
Directions: Graph each function below
Function: _________
Function: _________
Domain: __________________
Domain: __________________
Range: ___________________
Range: ___________________
Directions: For each graph below, determine it is a function
(what’s the vertical line test?). Then write the domain and range.
Finally, for each graph, find the output for the corresponding
input. Remember, there could be more than one!
Function: _______________
Function: _______________
Function: _______________
Domain: _______________
Domain: _______________
Domain: _______________
Range: _________________
Range: _________________
Range: _________________
(8)
f
=
________________
(2)
f
=
________________
(4)
f
=
________________
Function: _______________
Function: _______________
Function: _______________
Domain: _______________
Domain: _______________
Domain: _______________
Range: _________________
Range: _________________
Range: _________________
(2)
f
=
________________
(1)
f
=
________________
(7)
f
=
________________
Graph the function
2
()
fxx
=
on your calculator. Sketch the graph on the axis, and fill in
the table of values.
x
y
-3
-2
-1
0
1
2
3
x
y
-3
-2
-1
0
1
2
3
Look at the function,
2
()2
gxx
=+
. Graph this function on your calculator, sketch the graph on
the axis, and fill in the table of values.
How is this function different from the first one?
What do you think the function
2
()4
gxx
=-
looks like?
Check your guess on your calculator.
Use your calculator to graph each of the functions below, sketch
the graph on the axis, and describe how each one is different
than
2
()
fxx
=
.
1.
2
()3
gxx
=+
This is like
2
()
fxx
=
, but…
___________________________.
2.
2
()5
gxx
=-
This is like
2
()
fxx
=
, but…
___________________________.
3.
2
()(4)
gxx
=-
This is like
2
()
fxx
=
, but…
___________________________.
4.
2
()(5)
gxx
=+
This is like
2
()
fxx
=
, but…
___________________________.
5.
2
()(1)3
gxx
=-+
This is like
2
()
fxx
=
, but…
___________________________.
6.
2
()(2)5
gxx
=+-
This is like
2
()
fxx
=
, but…
___________________________
The basic function that we were working with is known as a
____________________ function. The “shifts”
(________________________) that we saw will occur in other
“parents” as well.
Linear
Square Root
Cubic
Quadratic
yx
=
yx
=
3
yx
=
2
yx
=
EXAMPLES Shifts
3
yx
=+
3
yx
=+
3
3
yx
=+
2
3
yx
=+
2
yx
=-
2
yx
=-
3
2
yx
=-
2
2
yx
=-
“Impossible”
5
yx
=-
(
)
3
5
yx
=-
(
)
2
5
yx
=-
“Impossible”
4
yx
=+
(
)
3
4
yx
=+
(
)
2
4
yx
=+
Directions: Name the parent function, and then describe the
translation that will occur.
1)
2
()1
fxx
=+
2)
(
)
3
()210
fxx
=--
3)
()1
fxx
=-
4)
()7
fxx
=+
5)
(
)
2
()3
fxx
=+
6)
()8
fxx
=-
Directions: Now, word backwards. I’ll give you the translation,
you write the function.
7)
()
fxx
=
Translate 5 units left and 1 units down
8)
2
()
fxx
=
Translate 1 unit down
9)
3
()
fxx
=
Translate 2 units left and 1 unit up
10)
()
fxx
=
Translate 3 units down
11)
()
fxx
=
Translate 6 units right
Wrap Up:
a) What is a parent function?
b) How do translations occur? Can we generalize those
translations?
c) Why is math so fun?
Warmup: Solve each inequality. Do not forget the rule that we
learned in the previous chapter.
a)
3111
x
->
b)
45
x
-³
c)
36
x
-<
d)
532
x
-<
Today we are going to discuss _______________________
inequalities. Basically this is just the combination of 2
inequalities onto one graph. There are ______ different cases to
consider.
OR( Shade both inequalities separately, but on the same
graph.
AND( Shade only the _________________ of the two graphs!
Let’s combine warmup problems a) and b) with OR, and c) and d)
with AND.
Practice:
Fancy: Combining an AND statement (
Now, work _____________________. I give you the graph, you come
up with the inequality.
8)
9)
10)
11)
Closure:
1) Describe the difference between an “AND” and “OR” compound
inequality
2) What is the one key you need to remember when solving
inequalities?
Extension: HW Start! The problems from the book are below.
The absolute value of a number is always ___________________.
The technical definition is the __________________ from ______.
Therefore,
2
-
= _____, and when
4
x
=
that means that
x
=
______ or _______!
Because numbers inside the absolute value can be _______________
or negative, we must account for two separate cases.
Example 1:
38
x
+=
Example 2:
2412
x
-=
Example 3:
216
x
+=
Example 4:
26
5
4
x
-
=
Example 5: Work backwards ( Answer is
53
x
=±
Warmup: Solve the two compound inequalities below and then
graph!
a)
3211
x
+>
or
412
x
<-
b)
7213
x
-<+£
When solving absolute value ________________________, we create
compound inequalities like the ones we saw in the warmup. There are
two distinct cases that cause the two cases: ____________ &
________.
CASE #1:
#
absval
<
(
CASE #2:
#
absval
>
(
Note: “or equal to” is treated the same!
a)
85
x
+>
b)
314
x
--³
In order to graph absolute value functions on your calculator,
when you’re in the functions list, push the MATH key, then the
right arrow to get to the NUMber submenu. abs( is the first
function on the list.
x
y
-3
-2
-1
0
1
2
3
Graph the function
()
fxx
=
on your calculator. Sketch the graph on the axis, and fill in
the table of values.
x
y
-3
-2
-1
0
1
2
3
Look at the function,
()2
gxx
=+
. Graph this function on your calculator, sketch the graph on
the axis, and fill in the table of values.
How is this function different from the first one?
What do you think the function
()4
gxx
=-
looks like?
Check your guess on your calculator.
Use your calculator to graph each of the functions below, sketch
the graph on the axis, and describe how each one is different
than
()
fxx
=
.
1.
()3
gxx
=+
This is like
()
fxx
=
, but moved…
___________________________.
2.
()5
gxx
=-
This is like
()
fxx
=
, but moved…
___________________________.
3.
()4
gxx
=-
This is like
()
fxx
=
, but moved…
___________________________.
4.
()5
gxx
=+
This is like
()
fxx
=
, but moved…
___________________________.
5.
()13
gxx
=-+
This is like
()
fxx
=
, but moved…
___________________________.
6.
()25
gxx
=+-
This is like
()
fxx
=
, but moved…
___________________________.
In general, we can say that the function
()
fxxhk
=-+
is like the
()
fxx
=
, but moved ________________________________________.
Another way we can say this is that it is the same shape as
()
fxx
=
, but with a new vertex at _______.
There are other translations that can happen to a parent
function:
1.
()
gxx
=-
3.
()34
gxx
=-
This is like
()
fxx
=
, but…
This is like
()
fxx
=
, but…
___________________________.
___________________________.
2.
()31
gxx
=--+
4.
1
()5
2
gxx
=+
This is like
()
fxx
=
, but…
This is like
()
fxx
=
, but…
___________________________.
___________________________.
Conclusion:
Tell whether the graph is the graph of a function. Then state
the Domain and Range for each in interval notation.
1.
2.
Function? ___________
Function? ___________
Domain: ____________
Domain: ____________
Range: _____________
Range: _____________
Show all your work, and evaluate each of the following for the
functions:
2
()23
2
()4
5
()
fxx
gxx
hxxx
=-
=-
=+
3.
(5)
f
-
4.
(5)
g
-
5.
(7)
h
6.
(1)(10)
fg
+
7. Consider the equation
()72
gxx
=+-
.
a) Describe how you would use the graph of
()
fxx
=
to graph the function
()72
gxx
=+-
. In other words, how would you move the original graph to
accurately place the new one?
b) What are the coordinates of vertex of g(x)?
8. What is a parent function? Use examples in your answer.
Solve, and graph your solution on a number line.
9.
591171261
xANDx
->+£
10.
915
743126
5
x
xxOR
-
+£->
11.
512233517
xxORx
+>--<-
Solve each equation.
12.
4101
x
--=
13.
43448
xx
+=+
14.
3612
x
-=
Solve each inequality, and graph your solution on a number
line.
15.
34
x
->
16.
223106
x
--+³
17.
351924
x
-+³
Write the equation of each absolute value function.
18.
19.
()
fx
=
__________________
()
fx
=
__________________
Answers!
1. yes, (-2, 4], (-3, 3]
2. no, [1, infinity), (-infinity, infinity)
3. -13
4. 6
5. 56
6. -1
7. a) left 7, down 2
b) (-7, -2)
9. (4, 7]
Directions: For each function below, please name the parent
function and the translation that is caused.
1)
2
()5
fxx
=+
2)
(
)
3
()31
fxx
=-+
3)
()2
fxx
=+
4)
()4
fxx
=-
5)
(
)
2
()2
fxx
=+
Directions: Now, word backwards. I’ll give you the translation,
you write the function.
6)
()
fxx
=
Translate 2 units left and 5 units down
7)
2
()
fxx
=
Translate 1 unit up
8)
3
()
fxx
=
Translate 9 units right and 1 unit down
9)
()
fxx
=
Translate 7 units up
10)
()
fxx
=
Translate 6 units right
11) Directions: Use the graph of each function to evaluate
()
fx
()
gx
a)
(
)
3_________
f
-=
(
)
6_________
g
-=
b)
(
)
1_________
f
-=
(
)
4_________
g
-=
c)
(
)
0_________
f
=
(
)
0_________
g
=
d)
(
)
2_________
f
=
(
)
1_________
g
-=
e)
(
)
5_________
f
=
(
)
0_________
g
=
12) Directions: Write the domain and range of each graph in
interval notation.
a)
b)
c)
Complete these problems from the textbook. Please be sure to
show your work and write the answer in the space provided.
Pg. 81, #1
Answer:
Pg. 84, #1
Answer:
Pg. 84, #2
Answer:
Pg. 171, #3
Answer:
Pg. 171, #6
Answer:
Pg. 174, #1
Answer:
Pg. 174, #7
Answer:
Pg. 174, #11
Answer:
U2 D1: Domain, Range, Relations vs. Functions & V. Line
Test
Date _________ Period_________
U2 D2: Function Notation, Indep./Dep. Variables &
Graphing
a)
b)
c)
e)
d)
U2 D3: Practice from Day’s 1 & 2
a) � EMBED Equation.DSMT4 ���
a) � EMBED Equation.DSMT4 ���b) � EMBED Equation.DSMT4 ���
U2 D5: Intro to Parent Functions
� EMBED PBrush ���
� EMBED PBrush ���
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� EMBED PBrush ���
� EMBED PBrush ���
� EMBED PBrush ���
� EMBED PBrush ���
� EMBED PBrush ���
U2 D7: Absolute Value Equations
U2 D6: Compound Inequalities
U2 D8: Absolute Value Inequalities
Date _________ Period_________
U2 D9: Absolute Value Functions – Graphs, Translations,
Refl.
� EMBED PBrush ���
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U2 D10: Unit 2 Review
� EMBED PBrush ���
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10. (-infinity, -4] or [5, infinity)
11. (-5, infinity)
12. -7, 15
13. -3/2, -1
14. -2, 6
15. (-infinity, -1) or (7, infinity)
16. [1/2, 5/2]
17. (-infinity, -4/5] or [6/5, infinity)
U2 D11: Unit 2 Review #2 with More Translations
U2 D12: Unit 2 Homework After the Test
Date _________ Period_________
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