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1

log a C = B is equal to:

A^b = C

2

Ex: log x 1/64 = 2 is the same as:

X^2 = 1/64
or
x = +/- 1/8

3

How do you solve for: log a (MN)

Product
log a (M) + log a (N)

4

How do you solve for: log a (M/N)

Quotient
log a (M) - log a (N)

5

How do you solve for: log a M^p

Power
P log a M

6

ln C = B is the same as:

e^b = C

7

e^b = C is the same as:

Natural Log
ln C = B

8

Ex: e^9 = y is the same as:

ln y = 9

9

Find common bases:
9^x-4 = 27

3^2(x-4) = 3^3

Drop the bases

You get: 2(x-4) = 3
Solve: x = 11/2

10

i^2 =

-1

11

Ex: log base 9 of 11 - log base 9 of 8 =

11/8

Remember Quotient rules (M/N)

12

Ex: log base 2 of 5 + log base 2 of 7 =

log base 2 of 35

Remember Product rules (MN)

13

Ex: log base 6 of 1/25 =

-2 log base 6 of 5

because 5^-2 = 1/25

14

Ex: 3x^2 - 6x + 1 = 0

How will you solve?

Quadratic Formula using the rule:
ax^2 + bx + c = 0

-b +/- the square root of (b^2 -4ac) ALL over 2a

15

What do they mean when asking if a function is "one-to-one" ?

One-to-one means that no 2 point have the same y-coordinate
(passes a horizontal line test)

16

For graphing with Asymptotes you will:

Plug and chug with x = -2, -1, 0, 1, 2

17

What is the Factor Theorem

(x=c) is a factor if and only if P(c) = 0

18

What is the Rational Zeros Theorem
Ex: 5x^4 + 7x^3 +4x^2 +4x - 3

With any polynomial the values with x^power must be in descending order

- Number with x^ greatest power is a0 (or p)
- Number with no x is an (or q)

p/q = a combination of any factors of p or q individually

Ex: a0 = -3, an = 5
p/q = -3/5 .... factors of -3 are +/- 1 and +/- 3, factors of 5 are +/- 1 and +/- 5

Therefore the answer(s) are: +/- 1, +/- 3, +/- 1/5, +/- 3,5

19

Finds a line given to points
Ex: (5, -6) (-1, 3)

1. Find slope (y2 - y1 / x2 - x1)
2. Put in y = Mx + b, use one given set of points to plug in and solve for b
ex: (3) = -3/2(-1) + b
3/2 = b

Line: y = -3/2x + 3/2

20

Steps to graphing a Quadratic Function:

1 Does it have a Minimum or Maximum
2. What x value does the min/max occur at
3. What is the vertex

1. If the Leading Coefficient is +, the graph will open UP and there will be a MINIMUM

To find the x calue and vertex:
x = - b / 2a

21

2x^2 - 4x + 1

Graph the quadratic function. Which way does it open and what is the vertex?

+ LC = opens UP
- LC = opens DOWN

x = - b /2a
Then plug and chug to find y-coord.