Test 2 (functions, exp, log, proofs) Flashcards
(35 cards)
Unit
values that we add to an operation that does not change the result
Injective in other words
one-to-one
Surjective in other words
onto
Identity function
y equals x
Reciprocal function
1 over x
Inverse square function
1 over x squared
What is the number in a logarithm called
argument
Which transformations are rigid
translations, reflections and rotations
Which transformations are non-rigid
stretches and shrinks
Vieta’s formulas
sum of roots equals -b/a; product of roots equals c/a
Fundamental theorem of algebra
every nonconstant polynomial has a complex root (therefore, every polynomal of degree at least 1 can be factored to linear factors)
Polynomials theorem 1
integer root divides constant coefficient of a polynomial
Polynomials theorem 2
polynomials have a root a / b, where a divides a0 and b divides an
Degree of a polynomial root
how many times it appears
Division theorem for polynomials
for dividing every polynomial by another polynomial there exist two other polynomials, so that one is a factor and the other the remainder
Remainder theorem
remainder when dividing a polynomial by x - a is equal to p(a)
Factor theorem
a polynomial has a factor (ax - b) iff p(b/a) equals 0
Vieta’s formulas for general polynomials
sum of root equals -(an-1)/an; product of roots equals (a0/an)*(-1)**n
Rational function
function of the form of the quotient of two polynomials
When is a rational function in a reduced form
if both polynomials have no common factor
What happens if we have a pole of an odd degree
graph will change sign
Where does a rational function intersect an asymptote
at the roots of the remainder
How is a curved asymptote called?
oblique asymptote
When do we have to check the solution of an equation?
if we squared it at any point; we used the rules of logarithms
