Practice and Problem Solving

Name
Date
Class
,~I
;
Domain, Range, and End Behavior
Practice and Problem Solving: AlB
Describe the interval shown using an inequality,
interval notation.
1. -I
I
($
I.
I I I I I I I
-4
-2
Inequality: Set Notation:
0
3:-,)<
X
of
Interval Notation:
2
"IX)
4
set notation, and
2. -I
X ~-
:,
I
($
I I I !
14
16.
Inequality:
18
I~
= _x2
22
~;t~
24
Set Notation: ~
j 5<: X"" .2 t-~
E 3) C'o)
Interval Notation:Q
5) 2
.
+ 3:
Domain: -
600Q .::.
t",J--
set
><: C"
I>C
Inequality:
X I-
Set Notationt
Interval Notation;
I'
28
26
1- :3 ~'x<:'f:1'D S
Describe the domain and range of the graph using an inequality,
notation, and interval notation. Then describe its end behavior.
3. Graph off(x)
I I I I I I •
20
DO
E-
l. XL"!?
-.3 _ ~
0
00) 60 )
:3
3 -~
Range:
Inequality: _(/QL~
'
Set Notation:
-
f )(~£~
Interval Notation:
C~()OI
~ .;
-3J
f:
33
End Behavior:
\
4s X-"/t><"'
t+~X -')
I-?'{~)-? -(.).0
- DQI f(IC.)
~-t>Q
Draw the graph of the function with its given domain. Then determine
the range using interval notation.
4. g(x)=-3x+2
with domain (-1, 2J:
"Y'-iT!
--,','
-;-"T'-r-"r,lJ
. ;-~,.,.--+ -'
)1 -
-,(-{)H
!
-I S
2
_(..1 l
i
; Xl
4
. ,
: -"j" .. ;0
)! I
.,
.J
i
•.. 1
~n...
_)("2)+2
;-
[----j.,."~
-'i'---'"'"'-~'-
-i'-'-~-:4-
t~t~:t~-r*.t.~~r_;_LL.~---i
Range:E.4
Original content [email protected]
J ~)
Houghton Mifflin Harcourt Additions
and changes to the original content are the responsibility
of the instructor,
Name
Da!e
Class
_
Domain, Range, and End Behavior
Practice and Problem Solving: C
For Problems 1-2, let fIx} = x2
-
4.
2. Determine the domain and range of f using set
notation and interval notation. Then describe its
end behavior.
1. Graph the function.
12 ; j
X! -
---G
R~ }
C>O ~
X .::o.Q~
tx;') 00 ')
l_u~,?-~4l
~~ __
LA
---G-4) J)
A<;, 'i -"';>
Q9 )
-Cry)
-+~
-)
As x ~ - 0>0) fl>C) -:;,~
oc
Home A uses 8 gallons of propane per day for heat. Home Buses
5 gallons per day. Both homes begin with propane tanks filled to
their maximum
Problems 3-6.
capacities
of 500 gallons. Use this information
for
3. Write two linear functions modeling the amount of propane remaining
in each tank per day. Then graph both functions on the same
coordinate plane.
HomeA
B(\{) ::500-~X.H~me
B:
9()<)~500 - 5X
~
C2 IS'"
-
,
-;':
.
A
5'0
100
0560
I()
!bU,' D
4. Describe the domain and range of each function using interval
notation.
D: 10 1"2.
V; ~I 'OcJ
g:_,So;:'7
<'1
«; @,15)6]
5. Write a function that describes th~bined
am~of
propane
Homes A and B have' remaining in their tanks per day. Use the
function to solve for x = 50, and interpret the result.
.
@lX) ~ fOOd - /3)<
'
9 (~)= It)
'5 00 - r,X
.
,
+ 500. -
'DO 0 =-/.:,
~
_12 ' [0) 7b.~
f "@/
/000]
2
~
ts
I(
3s-o
::po
1Pf,
Original content Copyright ~ by Houghton Mifflin Harcourt, Additions and changes 10the original conlent are the responsibility of the instructor,
@
-13
':""J3X
()O -13::'57,.;) -:: I DOD -
6. Write the domain and range of the function found in Problem 5 using
, set notati~n.
S ><
0 == IDOO
I
a
0 .
Name
Date
Class
Characteristics of Function Graphs
Practice and Problem Solving: AlB
Use the graph to answer Problems 1-4.
1. On which intervals is the function increasing and
decreasing?
-
,In
2. What are ttie local
ximum and minimum values?
/ I 4- )
rm',O ( J, 0 )
trrAy (-
3. What are the zeros of the function?
r;-J"O) (f,O)
4. What is the domain and range?
:'?i~l3J
;p-o]
~
_'
~
I
i
••
Shelley is studying the relationship b~tween her car's mileage (miles
per gallon) and speed (miles per'hour). The table shows the data
Shelley found. Use the table for Problems 5-7.
70
40
50 , 60
30
~~l~~~i,'wlJI~l~~~~!t}~~~~
iM~~tJ;~?triill~~'1:f~'inlftr~~;
.".-.v,,,..~.".....,.'.".'., ."".9•..,,,",,.h 34.0 33.5 31.5
5. Make a scatter plot of the data. Then use
a calculator to find an equation for the line
of best fit. Sketch the line.
Equation oflinej-=
(Ir~-
~
32
example of interpolation or extrapolation?
Explain.
" 28
~ij14ok-f-ll)h
:1i
5< ~5r1Yl
.r
24
~t
6e(~
&o~;n.
20
o
20
40
)),'
'_)../7.
..-'\..-
!
:FCS'5):: ~q "1 S or
qg ) Is the prediction found in Problem 6 an
- /\/ -"-I
.'--..: -
27.5
6. Use the equation found in Problem 5 to
predict the miles per gallon of Shelly's car
for a speed of 55 miles per hour.
-.lEX t 3q )6b~,
36
29.0
60
Speed (mph)
Original content [email protected] Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
6
)
\
-.
Name __
~
Date
Class
_
_
Characteristics of Function Graphs
Practice and Problem Solving: C
The table shows values of a polynomial
Problems 1-2.
function.
1
2.
3
15
12
41
2. Over which intervals is the average rate of
change negative?
-
1. Over which intervals is the average rate of
\
change positive?
[2,3"]
-013;
Use the table for
LO
c
CO)I]
1.]
JJ4?-J----
j
•
A fireworks projectile is launched at 20 meters per second from a
GO-meter cliff. The table shows the height, y, in meters the projectile
is above a field after x seconds. Use the table for Problems 3-9.
[@m~X~~5~~.~~)~~il3
75
7
6
B~l~ff~J(nr~t~T~jf.t;'
0
1
2
4
5
5
80
60
35
0
3. Make a scatter plot of the data. Then
use the QuadReg feature on a
calculator to find l} function that bestfils
the data. Sketch the function.
Functio~: ~
= ...6x ~+- ?-&\ +10 0
5. Over what interval is the projectile's height
increasing?
[0. 1:)
I
6. Over what interval is the projectile's height
decreasing?
@ J 5]
7. Use the equation found in Problem 3 to find
the height after 7 seconds. Does this
prediction make sense for the problem
situation? EXRlain.
S
~
Q~:W'\
60
.s::
.2' 40
~
---(7, -=-15) No Sen-se
I
~1~
.t,'J.~1-:J~~_t~-'r~j~~J.'~
,:J
.
:,
20
.
o
I
2
;
,
i
'
,
i
4
1
'
'
!
+
f
I
j
!X
6
8
- I
:;;
I
10
Time (sec)
4. What is the m Xim~m . ight of the
projectile?
'J..
rO
.:R )
Original
content
Copyright @ by Houghton Mifflin Harcourt. Addilions
I
and changes to the original content are the responsibility
7
of the instructor.