MULTIPLE CHOICE Choose the one alternative that best completes the statement or answers the question.
Find the equation that the given graph represents.
1)
1)
10
A)P(x)=*3* 4x2+x5
C) P(x):15 * 4*3  x2 + 3x 
5
B)P(x)=x3+x2+x+5
D)P(x):x3+ 4;p x5
SHORT ANSWER Write the word or phrase that best completes each statement or answers the question.
Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary.
2) t(x) = x3

7x2 +15x

25
Determine whether the statement is true or false.
3) If f(x) is a polynomial and f(5) = O then x + 5 is
Z) _
a factor of f(x).
3)
Sketch the graph of the polynomial function.
a)f(x):(x+2)3l
4)
Find the correct end behavior diagram for the given polynomial function.
5)P(x)=x53x38x+1
s)
\
\
Use the graph to answer the question.
6) Find the domain and range of the rational function graphed below.
10
8 6 4
2
I
6)
.1 68
t
t'
.. i I
\ \r in
\t, r'
liro
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Determine which of the rational functions given below has the following feature(s).
7) The xintercept is (5, 0)
A)f(x)=#
sir(*r
=i*
c)f(x)=#
7)
D)f(x):**
8) The yintercept is (0, 4)
6tt*l:#
8)
B)f(x):#
c)f(x):i3
D)f(x):#
9) There is a "hole" in its graph at x = 5
e)
f(x):i*
A)f(x)=#
B)
c)r(x)=#I
(x
+
dr rr*r _  5Xx 9)
(x+5)(x5)
10) The xaxis is its horizontal asymptote
A)f(x)
v
=
LL) xintercepts: (3, 0) and (3, 0),
asymptote: y =
6(,):*
B)f(x):#
)
10)
D)f(x)
=#
yintercept[O 9) vertical asymptotes: x : ]" and x = 1, horizontal
1
(x + 3Xx  3)
A) f(x) _
(x+1)(x1)
(x
+
O f(x) _  3)(x 3)
(x1)(x+1)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Answer the question
12) How can the graph of f(x)
=*
be obtained from the graph of y
2
=
1
7
12)
11)
Give the domain and range for the rational function. Use interval notation.
L
13) f(x)

(
1
13)
(x + 4)2
Give the equations of any vertical asymptotes.
r1)
f(x)=#
74)
1s)f(x):*
1s)
Give the equations of any horizontal asymptotes.
16)g(x)=#
17)h(x)
=9xz
'l*'
18)s(x)
=#
1b)
17)
8
18)
Give the equation of any oblique asymptotes.
19) h(x)
6
 5x+2
= 3xzlx
7e)
20)f(x)=#
20)
Identify any vertical, horizontal, or oblique asymptotes in the gfaph of y= f(x). State the domain of f.
27)
21)
10 8 6 4
2
J
\
\
Sketch the graph of the rational function.
22)
f(x)=:+
22)
Solve the problem.
23) If the average cost per unit C(x) to produce x units of plywood is given
what is the unit cost for
ty C(x)=ffi,
23)
20 units?
Determine whether or not the function is onetoone.
24)
24)
2s)
4
\
Decide whether the given functions are inverses.
26) f = lF3, 6), (0,4), (4, 3), (8, 10)l
g= le6, 3), (4,0),(3,4), (10, 8))
26)
Use the definition of inverses to detennine whether f and g are inverses.
27)t(x)=2x4,
28) f(x)
=7x
7,
g$)=+
g(*)
=*
27)
*1
28)
If the function is onetoone, find its inverse. If not, write "not onetoone."
29) l(L9,5), (1O L), (19,7)l
2e)
30) l(7, 7), (6, 7), (5, 3), (4, 9\l
30)
31) f(x) =6x3 + 4
31)
32) f(x)
32)
=2x+3
Find the function value. If the result is irrational, round your.rnswer to the nearest thousandth.
33) Let
f(x):4x.
34) Let
(.):f+l..Find
Find f(3).
33)
(3).
34)
L'J
Evaluate the logarithm.
3s) log,
1
fr
35)
Write an equivalent expression in exponential form.
36)
log'
625
=4
36)
Write in logarithmic form.
3n
22
:!
J/)
Solve the equation.
38)tos7$=x
38)
Use the properties of logarithms to rewrite the expression. Simplify the result
if possible. Assume all variables represent
positive real numbers.
39) 1o9614x6y)
3e)
5
Write the expression as a single logarithm with coefficient
1. Assume
all variables represent positive real numbers with
a+1and b*L.
40) (logn x
 logs y) + 5 logx z
40)
Solve the system by substitution.
41)x+Y=2
41)
xY=8
Solve the system by elimination.
42) x 3y:8
6x  4Y =)/
42)
Solve the system by substitution.
43) x+7y=27
13)
6x+7Y=$/
If the system has infinitely many solutions, write the solution set with x arbitrary.
44)5x8y=1
Solve the system.
10x +
1'6Y
Write the augmented matrix for the system. Do not solve the system.
45) 7x+ 4y= J)
5x+ 3Y:
46)
6x
))
+22= 1.0
4y+72= 26
9x + 3y
44)
=1
+72:
4s)
46)
32
Use the GaussJordan method to solve the system of equations.
If the system has infinitely many solutions, give the
solution with y arbitrary.
47)x+y=J
47)
*Y=4
Use the Gaussordan method to solve the system of equations.
variable be the arbitrary variable.
48)
7x9y z=24
x3y52=54
2x+ y+ z= 7
If
the system has infinitely many solutions, let the last
48)
Find the value of the deterninant
_r)
4e)
l:;l
ls+t
50)lasz
s0)
lr+s
6
\
1314 REVIEW TEST4 FpJLZOI7
1)D
2) 5,7 + 2i,7
3) True

2i
4)
v..........
..".....5
r'l
. l.*
...t,
'
'5'
.
5)
*o
6j Domain:
(,
2) u (2,
*\
Range:
(, 3) u (3' )
7)B
8)A
e)D
10)
11)
c
A
By making a horizontal shift of 6 units to the right
13) Domain: (, 4) v (4, *\ Range: (0, )
12)
14) x
2
=f,
15)x=3,x=3
16) none
17)y=3
18)y=0
19) none
20)y=1ag
21) Vertical: x
=2;horizontal: y = 4;
('*,2)
u
(2'
*)
22)
.lA
.8. .6.
23) $18.00
24) No
7
\
Answer Key
Testname: MATH 1314 REVIEW TEST4 FALLZOIT
25) Yes
26) Yes
27) No
28) Yes
29) l(5 , 79) , (7 , 70),
(7
, 79)l
30) not onetoone
31) f1(x) =
32) f1(x)
zffi
^l\l6
=+
33) 64
zqt1:rx
3s) 2
36) 54 = 625
37)
togrj.=z
38) {2}
39) logu4 + 6logax + logaY
4o)rog2ttrl
41) {(5,3)}
42)
\V,s)l
43) t(6,3))
44) a
4s)
46)
tliE l
l":l;21
lo z zlzz l
44{ +,+\
48)
{(3,4,9)l
4e) 62
s0) 6
8