**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!!!

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