# Properties of Polynomial Function Graphs

```Name:
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Properties of Polynomial Function Graphs
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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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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
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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
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asx+-oo,y*-_
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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.
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A.
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- 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.
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SEred ofl lhe groph..-
polynomioii
cir4ffiSnr dlsconl:nuous
b) llre Ieoa;ng coeific;enl
the degree
ts
functions?
positive o' negctive?
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circle the
poinl
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the point
block
purple
notst,bn wi'lh x-volues,f
(- l.s, -.b) u (1, 0o)
# of tp's:
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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)
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Code
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finterval NotationJ
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Domain { x- valuesJ
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fthe point
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x- interceptfsJ
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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
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t
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color
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Term
Point(s) or Interval(s)
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Degree?
Odd or Even?
or Negative?
End Behavior
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Domain Ix- vaiues)
{
finterval Notation)
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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 ?
or Negative?
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Positive
End Behavior
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Domain
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Ix- valuesJ
\$nterval NotationJ
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Range [y-values]
(Interval NotationJ
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Green
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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
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Point(sJ or IntervalfsJ
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or Even?
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or Negative?
End Behavior
x*-*,y*
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Domain (x- valuesJ
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[Set NotationJ
Range fy-valuesJ
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[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
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Term
L\o
Code
Point[sJ or lnterval[s)
Degree?
Odd or Even?
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
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t:
Write the domain in set notation.
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1.
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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
```