MATH 1120
Section 6.5, Properties of Logarithms
Week 12 (6.5, 6.6)
y=log a x
iff
For Exam 5
x=a
y
MATH 1120
. log a 1=0
Week 12 (6.5, 6.6)
For Exam 5
. log a
. log a a=1
( MN )=log M log N
a
a
r
. log a M =r log a M
. a log M =M
a
. a x =e x ln a
r
. log
MATH 1120 Week 13 (6.7, 6.8, 12.1, 12.2) For Exam 5
Section 6.7, Financial Models
.1=Prt _,.e:(1+:)"_1
.A =P*(1+%)nt
TC
.Azpe
1. Set up the equation to find the amount that will result from each investment:
W $50 invested at 6% compounded saga/o coumpound
MATH 1120 Week 12 (6.5, 6.6) For Exam 5
Section 6.5, Properties of Logarithms y = loga x iff x = ay
_ M
.loga 1 0 .loga (W) = loga M 10ga N
Jog a z 1 .loga MT 2 r loga M
'alogaM = M 'ax = exlna
log. a = r 10 M
g
logaM = 10; a
.loga(MN) : loga M + loga
MATH 1120 Week 15 (12.5, 11.1 and 11.2) For Final Exam
Section 12.5, Partial Fraction Decomposition
Partial fraction decomposition has 4 basic rules to follow in order to decompose proper rational expressions.
In any case consider the fraction PE:%
P(x)_
MATH 1120 Week 08 (5.2 & 5.3) For Exam 4
Section 5.2, Rational Functions (properties)
Definition of a Rational function:
1706)
W ) where p(x), q(x) are polynomial functions, q(x) is not a constant, and p(x) IS not zero.
Function R(x)
Determine whether th
MATH 1120 Week 09 (5.4, 6.1, 6.2) For Exam 4
Section 5.4, Polynomial and Rational Inequalities
Solve the inequalities with polynomial/ rational functions by graphing or 1.) x Intercepts 2.) Determine + or
.(1 x)2(x + 4)2(x 5)2 S O
:
MATH 1120 Week 02 (R.6 Ch 1.5) For Exam 1
Section R6, Synthetic Division
Use synthetic division to divide the polynomials:
2x3+12x24x~66 +x+3 2x3x2+3 + x3 ' 6x3+5x2+10x+ + x+%
31403 5681036
5 IS 15 *2 fl dz/z
W W
:1 b '5 6 Q 0
Mwwmwww
Section 1.1, Lin
if MH" 20 ,., - v \NeeK 0 (fh 343319) Far Exam :2
Section 3.3
A function f is increasing on an open interval 1 if, for any choice ol 3:. and x2
in I. with xi < .\'2. we have fix!) < HA3).
A function f is even it. tmuvcry nulnhur .\' in its clonu
/V\ ulh 20 . \NQK 05 [d1 3a331) , (for EXAM Q 2
Section 3.3 ;
i
' A function I is even il. for every 11111111101 1' in its dmnnin.
the number 1' is also in the domain 11ml 1
- A function I is increasing on an open interval I if 101 21155 choice Oi x, and
MATH 1120 Week 04 (Ch2.5) For Exam 2
Section 2.5, Variations
Write the equation which represents the phrase below (eg. y = 8x)
y varies directly with x. When y = 2, x = 6
r: x
- WWI V
21Kt Kt Vi/ i
3 l
p varies inversely to q. When p = E q = 4
pw K , ,
.3
VWKl
Section 6.3, Exponential Functions
a. Rangeofthefuncon c. x_hwecept(s)
b. Horuontalasynunote d. 3Ljntercept(s)
006) = 62 4906) = 5 ~ 6"
f(oJ)
X 4
\/1 C +
I?" 9" (OH)
\I/ vs, 6:, \LM
,2( i
\/ 3 jg (u I)
[i
e.
Graph
E, Ean "I a. Rangeofthefunction c.
MATH 1120 Week 14 (12.6, 12.7) For Exam 5
Section 12.6, Systems of Nonlinear Equations
Solve the systems using Substitution, Elimination, or Graphing
cfw_y2x2i1 cfw_yz
'y=x+1 'y
5;! EJ4 ArHon '_
Xfi = KW
cfw_ 35:23] cfw_31:396-5 IULH,V)VM~'I'0/\A
'x=y
MATH 1120
Section 6.7, Financial Models
. I=Prt
Week 13 (6.7, 6.8, 12.1, 12.2)
For Exam 5
r n
1
. r e = 1+
n
( )
nt
( nr )
. A=P 1+
r
. A= p e
. r e =e 1
rt
1. Set up the equation to find the amount that will result from each investment:
$ 50 invested at
MATH 1120
Week 16 (11.3, 11.4, and 13.1)
For Final Exam
Section 11.3, The Ellipse
The Ellipse is comprised of 7 parts: 2 foci (points), 4 vertices (points), and a center (point)
Write the follow in Standard Form. What are the foci, vertices, and the cente
MATH 1120
Section 6.3, Exponential Functions
a. Range of the function
b. Horizontal asymptote
f.
Week 10 (6.3, 6.4)
c.
For Exam 4
x intecept (s)
. Q ( x )=e x+2
h.
i.
j.
k.
l.
m.
n.
o.
p.
q.
r.
s.
t.
u.
v.
w.
x.
y.
z.
aa.
ab.
ac.
a._
b._
ad.
c._
d._
ae.
y
MATH 1120
Week 15 (12.5, 11.1 and 11.2)
Section 12.5, Partial Fraction Decomposition
For Final Exam
MATH 1120
Week 15 (12.5, 11.1 and 11.2)
For Final Exam
Partial fraction decomposition has 4 basic rules to follow in order to decompose proper rational exp
MATH 1120
Week 02 (R.6 Ch 1.5)
Section R6, Synthetic Division
Use synthetic division to divide the polynomials:
For Exam 1
.
3
2
2 x +12 x 4 x66 x +3
.
3
2
2 x x +3 x3
.
9
1
6 x 3+5 x 2 +10 x+ x +
2
2
Section 1.1, Linear Equations
Solve for the unknown va
MATH 1120
Week 04 (Ch2.5)
Section 2.5, Variations
Write the equation which represents the phrase below (eg. y=8 x )
y varies directly with x . When y=2 , x=6
p varies inversely to q . When
r varies jointly with t and
f
is
A
3
,
2
q=4
z . The constant is
v
MATH 1120
Week 08 (5.2 & 5.3 )
Section 5.2, Rational Functions (properties)
Definition of a Rational function:
R ( x) =
Function
p(x)
q(x)
For Exam 4
p ( x ) , q( x) are polynomial functions, q( x) is not a constant, and
where
p( x)
is not zero.
Determine
MATH 1120
Week 14 (12.6, 12.7)
Section 12.6, Systems of Nonlinear Equations
Solve the systems using Substitution, Elimination, or Graphing
For Exam 5
.
cfw_
y=x 2+1
y=x +1
.
y = x
cfw_ y=2x
.
y
cfw_x =x=2
y 2 y
.
x5
cfw_ y=3
x + y =5
2
2
2
MATH 1120
.
cfw
MATH 1120
Section 5.1, Polynomial Functions
Definition of a polynomial function:
1.) domain ( , )
Week 07 (5.1, 5.5, 5.6)
2.) continuous 3.) smooth 4.)
For Exam 3
n
f ( x )=a n x + a0 x
0
(n is a natural number)
Determine whether the following is a polyno
MATH 1120
Week 09 (5.4, 6.1, 6.2)
Section 5.4, Polynomial and Rational Inequalities
Solve the inequalities with polynomial/ rational functions by graphing or 1.)
For Exam 4
x Intercepts 2.) Determine + or
. x ( x4 )3 ( x +2 )2 0
. ( 1x )2 ( x +4 )2 ( x 5
MATH 1120 Week 04 (Ch2.5) For Exam 2
Section 2.5, Variations
Write the equation which represents the phrase below (eg. y = 8x)
y varies directly with x. When 3/ = 2, x = 6
p varies inversely to q. When p = S, q = 4
1
r variesjointly with t and z. The cons
MATH 1120
Week 07 (5.1, 5.5, 5.6)
Section 5.1, Polynomial Functions
Definition of a polynomial function:
1.) domain: (00, 00) 2.) continuous 3.) smooth 4.) f(x) = anx + + aoxo (n is a natural number)
For Exam 3
Determine whether the following is a polynom
MATH 1120 Week 16 (11.3, 11.4, and 13.1) For Final Exam
Section 11.3, The Ellipse
The Ellipse is comprised of 7 parts: 2 foci (points), 4 vertices (points), and a center (point)
Write the follow in Standard Form. What are the foci, vertices, and the cente