### Present Remotely

Send the link below via email or IM

• Invited audience members will follow you as you navigate and present
• People invited to a presentation do not need a Prezi account
• This link expires 10 minutes after you close the presentation

Do you really want to delete this prezi?

Neither you, nor the coeditors you shared it with will be able to recover it again.

# College Algebra Final Review

Everything my MAT 117 students learned in six weeks
by

## Jordan Nguyen

on 17 July 2013

Report abuse

#### Transcript of College Algebra Final Review

MAT 117 College Algebra
JBMSHP Summer 2013
Functions
What is a Function?
Polynomial
& Odd Root
Rational
Even Root
Difference Quotient
Average Rate of Change
Domain
Transformations
Linear
Asymptotes
Composite & Inverse
Absolute Value
Greatest Integer
Piecewise
Zeroes
Exponential
& Logarithmic
More
Applications
Compound Interest
Exponential Growth & Decay
Logistic Models
Systems
Arithmetic
Geometric
Domain:
All Real Numbers
(- , )
8
8
Domain:
All Real Numbers excluding "bad seed"
Set Denominator to Zero & Solve for x
(Can't Divide by Zero)
Domain:
x values that make expression under radical 0
(can't be non-real)
Domain:
x values that makes expression in log > 0
Factoring & Expanding (FOIL)
Parabola Opens Up/Down
Find Vertex (h, k) - Max/Min
Axis of Symmetry
Standard Form:
(Complete the Square)
find f(x), given x
find x, given f(x)
f + g, f - g, f * g,
Set AND Interval Notation
Remember Special Case?
Graphing
Even, Odd, or Neither
Identify Increasing/Decreasing/Constant Intervals
Finding Local Minimum/Maximum Values
Horizontal/Vertical Shifts
Horizontal/Vertical Stretch/Compression
Reflections
Slope-Intercept: y = mx + b
Point-Slope: (y - y ) = m(x - x )
Applications
Max # of Turning Points
Near Behavior
End Behavior (Power Function)
Highest Degree
Long Division!
Remainder & Factor Theorem
Rational Zeroes Theorem
Fundamental Theorem of Algebra
Complex Numbers
Solve Polynomial Equations
Synthetic Division
1) Domain
2) Intercepts
3) Asymptotes
4) Plot Points
5) Graph!
Evaluate Exp & Log Fun
Convert Expressions (Twist Method)
Properties of Log:
Write as Sum/Difference of Logs (Expand)
Write as Single Log (Compress)
log (M ) = p log (M)
log (MN) = log (M) + log (N)
log ( ) = log (M) - log (N)
Effective Rate
Supply & Demand

Profit = Revenue - Cost
Revenue = quantity * price
Break Even Point
I = P r t
Half-Life
Substitution
Elimination
Matrices
a = a + (n - 1)d
a = a * r
Only when Converge
New Material
(Series & Sequences)
Jordan.N.Nguyen@asu.edu
KNOW
EVERYTHING!!!

THANK YOU!!!
GREAT JOB &
F
antastic!!!
+
http://www.mathforum.org/dr/math/
Dr. Math
DON'T FORGET TO BREATHE ! ! !
Get Plenty of Sleep ! (Recommended 8 hours)
Eat Breakfast ! !
(Relax & Keep a Cool Head)
(f g)(x)
(g f)(x)
(f f)(x)
(g g)(x)
(f o f )(x) = (f o f)(x) = x
-1
-1
y = x
y = x
y = x
y = x
y = x
y = x
y = |x|
2
3
1/3
1/2
Degree 3 or higher
f(x + h) - f(x)
h
D.Q. =
A.R.C. =
f(x) - f(c)
x - c
from c to x
use Calculator to:
Graph Functions & Scatter Plot
Find ("Calc") Values
Find Linear Regression Line
Reduced Row Echelon Form
Multiplicity
odd = cross
even = touch (bounce)
{
R(x) =
p(x)
q(x)
x = zero of q(x), but not p(x)
let: t = degree of p(x)
b = degree of q(x)
t < b, y = 0
t = b, y = ratio of leading coefficients
t > b, none
t = b + 1
{
Vertical*
Horizontal
Oblique (Slant)
f(x) = a(x - h) + k
f(x) = D(x)Q(x) + R(x)
when D(x) = x - c, R(x) = f(c)
(x - c) is a factor iff R(x) = f(c) = 0
possible zeroes:
degree = # of complex zeroes
h =
-b
2a
-1 < r < 1
Domain
1. Find Domain of Inner Function
2. Find Domain of Outer Function
3. Set Equal to Inner Function
4. Solve for x & Exclude from Domain
2. Find Composite Function
3. Find Domain of Composite Function
4. Include in Domain
D = R R = D
f
f
f
f
-1
-1
b
b
b
b
b
b
b
b
b
log (M) =
log (M)
log (b)
x
x
p
M
N
Change of Base:
A = P (1 + )
A = Pe
S = (a + a )
S = a
S =
r = 0, 1
f(-x) = f(x)
f(-x) = -f(x)
r
n
nt
rt
A(t) = A e
kt
0
I = A - P
= t, when A(t) = A
1
2
0
P(t) =
c
1 + ae
-bt
n
n
n
n
n
n
1
1
1
1
1
n
2
n - 1
1 - r
1 - r
a
1 - r
8
2
2
1
1
p
q
1. replace f(x) with y
2. swap x & y
3. solve for y
4. replace y with f (x)
-1
f
g
O

O

O

O
b = x, so log x = y
y
b
a = a , then u = v
u v
f(x) = ax + bx + c
(Difference between an x-intercept)
Determine Symmetry
1
2
3
*this is partially correct
Other
-1
Steps for Rational
(step)
4
5
6
Any Questions?
Double & Triple Check your Work
Full transcript