Exercise Set 4.1: Polynomial Functions
−6 −4 −2 2 4
6
−10
10
x
y
−4 −2 2 4 6
8
−10
10
x
y
−4 −2 2
40
40
80
x
y
−4 −2 2 4
−40
40
x
y
−2 2 4
−200
200
x
y
−2 2 4
1200
−800
−400
400
x
y
Sketch a graph of each of the following functions.
1. 3
)( xxP =
2. 4
)( xxP =
3. 6
)( xxP =
4. 5
)( xxP =
5. .0 and odd is where,)( >= nnxxP n
6. .0 andeven is where,)( >= nnxxP n
Answer the following.
7. The graph of 23 )4()2)(1()( +−−= xxxxP has x-
intercepts at .4 and ,2,1 −=== xxx
(a) At and immediately surrounding the point
2=x, the graph resembles the graph of what
familiar function? (Choose one.)
x
y= 2
xy = 3
xy =
(b) At and immediately surrounding the point
4−=x, the graph resembles the graph of
what familiar function? (Choose one.)
x
y= 2
xy = 3
xy =
(c) If )(xP were to be multiplied out
completely, the leading term of the
polynomial would be: (Choose one; do not
actually multiply out the polynomial.)
66554433 ;;;;;;; xxxxxxxx −−−−
8. The graph of 32 )5()3()( −+−= xxxQ has x-
intercepts at .5 and 3 =−= xx
(a) At and immediately surrounding the point
3−=x, the graph resembles the graph of
what familiar function? (Choose one.)
x
y= 2
xy = 3
xy =
(b) At and immediately surrounding the point
5=x, the graph resembles the graph of what
familiar function? (Choose one.)
x
y= 2
xy = 3
xy =
(c) If )(xP were to be multiplied out
completely, the leading term of the
polynomial would be: (Choose one; do not
actually multiply out the polynomial.)
66554433 ;;;;;;; xxxxxxxx −−−−
Match each of the polynomial functions below with its
graph.
9. )4)(1)(2()( +
+
−
=
xxxxP
10. )4)(1)(2()( −
−
+
−
=
xxxxQ
11. 22 )4()1)(2()( ++−−= xxxxR
12. )4)(1()2()( 2++−= xxxxS
13. )4()1()2()( 32 −−+= xxxxU
14. 233 )4()1()2()( −−+−= xxxxV
Choices for 9-14:
A. B.
C. D.
E. F.
