Gen. Math

by dutch orellosa

1. FUNCTION

1.1. y=a number

1.2. vertical test line

1.3. 1 input = 1 output

1.4. domain of a function

1.4.1. always look at denominator

1.5. f(x)=4x^3-2x D= (-infinity, infinity)

2. Relations and Functions

2.1. all functions are relation

2.2. x-input: independent; y-input:dependent

2.3. graph

2.3.1. discrete graph

2.3.2. continuous graph

2.4. f(x)

3. Business Math

3.1. Simple interest

3.1.1. I=Prt

3.1.2. F=P=Prt

3.2. compound interest

3.2.1. F=P(1+i)^n

3.2.2. P=F(1+i)^-n

3.3. Annuity

3.3.1. kinds

3.3.1.1. simple

3.3.1.2. general

3.3.1.3. deferred

3.3.2. formula

3.3.2.1. F=R((1+i)^n-1/i)

3.3.2.2. P=R(1-(1+i)^-n/i)

4. rational function

4.1. f(x)=P(x)/Q(x) P(x) is polynomial Q(x) is not equal to 0

4.2. vertical aymptote

4.3. horizontal/oblique asymptote

5. Inequality

5.1. factor *if fraction, factor both num and den

5.2. table of values

5.3. test values

5.4. x^2-x>2

6. inverse function

6.1. different input produce same output inverse is not a function

6.2. one to one

6.3. x+2/x+1

7. exponential function

7.1. f(x)=b(x) b>0,=!1 b can't be negative

7.2. natural exponential

7.2.1. e=2.71828183

8. logarithm

8.1. b>0 and is not equal to 1

8.2. logbn=p if and only if b^p=n

8.3. logarithmic properties

9. systems of linear equation

10. Logic

10.1. system based on proposition

10.1.1. types of proposition

10.1.1.1. conditional

10.1.1.2. converse

10.1.1.3. inverse

10.1.1.4. contrapositive

10.1.1.5. biconditional

10.2. logical operators

10.2.1. negation(NOT) [-]

10.2.2. conjunction(AND) [^]

10.2.3. disjunction(OR)[v]

10.2.4. exclusive or(XOR)

10.2.5. implication

10.2.6. biconditional

10.3. inference rules

10.3.1. rule of addition

10.3.2. simplification

10.3.3. conjunction

10.3.4. modus ponens

10.3.5. modus tollens

10.3.6. hypothetical Syllogism

10.3.7. disjunctive syllogism