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College Algebra Final Review

Everything my MAT 117 students learned in six weeks
by

Jordan Nguyen

on 17 July 2013

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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
Quadratic
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
Leading Coefficient
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.khanacademy.org/
http://www.mathforum.org/dr/math/
Dr. Math
Khan Academy
Last Minute Advice
DON'T FORGET TO BREATHE ! ! !
Get Plenty of Sleep ! (Recommended 8 hours)
Eat Breakfast ! !
READ YOUR NOTES!!!
Study Your Tests, Quizzes, &
(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:
Check Your Work
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
Additional Resources
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