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