Properties of Polynomial Function Graphs

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Name:
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Properties of Polynomial Function Graphs
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Domain:
Range:
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Interval Notation: uses parenthesis or brackets to imply where the function is defined
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Set NotatiglirUses sets to say explicitly where the function is or isn't defined
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Domain
(Interval
Notation)
Domain
(Set Notation)
Range
(lnterval
Notation)
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For the graphs below, write the domain and range in interval and set notation.
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Name:
Date
Period:
Practice Worksheet: End Behavior & Graphing Polynomials
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WITHOUT graphing, identify the end behavior of the polynomial function.
lly=zxs+7x2+4x
Degree:_
Sign of
LC:-
3)y=12x4-2x*5
2) Y ='5x
Degree:_
Sign of
LC:_
Degree:_
Sign of
[email protected],y-_
aSX+-oo.y-_
[email protected],y-_
as x ---+ oo, Y
41 ,*-A-Zx-+x2+5x3
asx+co.y-
asx---+6,y+
5)y=1*2x6-4x2-2x6
6ly=4x+2-5x6
Standard Form:
Standard Form:
Standard Form:
Degree:_
Sign of
LC:-
Degree:_
Sign of
LC:_
Degree:_
LC:_
LC:_
Sign of
[email protected],y--
[email protected],Y-_
asx+-oo,y*-_
[email protected],Y*
asx---+m,y+
[email protected],y*
Match the polynomial function with its graph WITHOUT using a graphing calculator. Think about how the degree of the
polynomial affects the shape of the graph.
B.
A.
C.
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t
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t
!=-2x3 *3x*1
-7)Y=-x2+4x
!=-x4+3x2+3
-l0l 131 v=!*+-1*z
22
-81
l4l v=1rt-Zx3+2x
-111Y=3x2+2
55
1^.4
9l v = :x'33
l2l v=?x-+
3
!=-5x*2
-151
\
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It
1
2
- Use the groph below to fillin lhe missing informotion from lhe loble.
- lobelthe groph by using lhe oppropriote CODE ond TERM.
Term
Definilion
Point(s) or lntervol{s}
The highesl point on o groph in o
Locol
given orec,
Moximum
The lowesi point on o groph in o
Locol
given oreo.
Minimum
Absolule
Moximum
The highesl poinl on the entire
Absolule
Minimum
The lowest point on the entire
domain of o function.
domoin oi o function.
xintercept(s)
The point{s} ct which the groph
crosses the x-oxis.
y-inlercepl
The point ot which the groph crosses
lntervol(s)
of lncresse
An iniervolin which the y-volues ore
increcsing.
fUs* inlervol nolafon with x-volues/
lntervol(s)
of
Decreose
An intervolin which lhe x-vclues cre
decreosing.
{Use rntervol
{D, 3)
chonges frorn increcsing lo
decreosing ond vice verco.
I
I
/
SEred ofl lhe groph..-
polynomioii
cir4ffiSnr dlsconl:nuous
b) llre Ieoa;ng coeific;enl
the degree
ts
functions?
positive o' negctive?
odd?
circle the
poinl
Square
the point
block
purple
notst,bn wi'lh x-volues,f
(- l.s, -.b) u (1, 0o)
# of tp's:
/
blue
yellow
The points ot which the groph
II t
c)
(-5, o), [-z,o),[r, o), (i,o
the y-oxis-
Turning
Point(s)
o)
('s.t,Q ; (s, e)
f.5, -r.s)
(r,g)
no nf, (."9 tc chau;or)
Code
3
rar-1
)
Term
Point(sJ or Interval[sJ
Degree?
Odd or Even?
Code
,5
i
5
:
Leading Coefficient? Positive
or Negative?
Posinv
Lef
+
Pignl
x9-oo,y*
x)
oo,
s
U
(- oo
Range (y-valuesJ
:
.
t
0O
q
I
oo)
f:rb,m)
flnterval NotationJ
a
..
_tq
,
I
i
Local Maximum
Local Minimum
/Absolute Maximum
s
(>
:
y* @
finterval NotationJ
B
:
:
(
Domain { x- valuesJ
e
q
1,
a
End Behavior
?
l\
A
6ren
a
(
o
5
(-t
)
,-t)
Green
:
(tl,'
0)
2b)
Blue
t
t
gnd
lCircle
fthe point
(t , -zu)
x- interceptfsJ
Square
the point
Black
y-intercept
Purple
Tangent Point
fTurning Point where the
graph touches the x-axis but
does not cross it]
Choose a
Absolute Minimum
Ns\q. (
t
;
(t 'c)
t '?"-'o'
color
j
-?5
1( *+ r)z (x- D (x -u)
Term
Point(s) or Interval(s)
+s
Code
Degree?
Odd or Even?
Leading Coeffi cient? Positive
or Negative?
End Behavior
x* -*,y*
xlm, y+
Domain Ix- vaiues)
{
finterval Notation)
*
Range fy-vaiuesJ
(lnterval NotationJ
Maximum
x
Green
Local Minimum
Blue
Absolute Maximum
Circle
the point
Absolute Minimum
x- intercept[sJ
Square
the point
Black
y-intercept
Purple
Tangent Point
(Turning Point where the
graph touches the x-axis but
does not cross it:J
Choose a
color
q
-Zx L +\
Point[sJ or lnterval[sJ
Term
Codt
t:
Odd or Even ?
Leading
or Negative?
P
(0
Positive
End Behavior
x*-co,Y+
(Lr.s2s 2.9sij)
xloo,y)
Domain
.1)
z
Ix- valuesJ
$nterval NotationJ
(-1
.:
.ils7, li)
il
Range [y-values]
(Interval NotationJ
.-,
Green
x5-Z*+'l
Local Maximum
Blue
Local Minimum
Absolute Maximum
Circle
the Point
Square
Absolute Minimum
i-
the
Black
t
intercePt[ sJ
Purple
y-intercePt
Tangent Poi nt
(Turning Poin t where the
graph touches the x-axis but
does not cross
Choose a
color
7
Term
AJ
i-i :rrr +;r:r1
Point(sJ or IntervalfsJ
?
or Even?
!
Leading Coefficient? Positive
or Negative?
End Behavior
x*-*,y*
x) m, y*
io, o)
-{
l-? 7:ril fi\
Domain (x- valuesJ
-2
(2 236,
-n
[Set NotationJ
Range fy-valuesJ
{i.2!.i1. -.1.3c-r)
[Set Notation]
Local Maximum
Minimum
-\-
I
Green
BIue
Absolute Maximum
Circle
the point
Absolute Minimum
x- intercept(s)
Square
the point
Black
y-intercept
Purple
Tangent Point
(Turning Point where the
graph touches the x-axis but
does not cross itl
Choose a
color
y3-b
rl
\
Term
L\o
Code
Point[sJ or lnterval[s)
Degree?
Odd or Even?
Leading Coefficient? Positive
or Negative?
End Behavior
.I
-2
x*-ao,y+
xlm, y+
^1
Domain I x- values]
[Set Notation)
a
:
Range {y-values}
[Set Notation)
Local Maxirnum
Local Minimum
Absolute Maximum
Absolute Minimum
x- intercePtfs)
y-intercePt
Tangent Point
(Turning Point where the
graph touches the x-axis but
does not cross
V
Green
BIue
Circle
the point
Square
the point
Black
Purple
-Lxq+ .{ xL -
L
'3
-q
t:
Write the domain in set notation.
\^
1.
,,\
Z.Write the range in interval notation.
'J/
,r,1S. Consider the properties of the function
f (x)
=
*xzQ( + a)(x
- 1)
**** Graph this function using Desmos.com/calculator
Select True or False for each statement about the graph of the function.
A.
It is tangent to the x-axis at x=0
True
False
B. It crosses the x-axis at x=4
True
C.
D.
,
False
It has two local maximum values.
True
False
It has no global minimum
True
False
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