Flashcards in Final Deck (21)

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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