Test 2 (functions, exp, log, proofs)

Question 1

Unit

Answer 1

values that we add to an operation that does not change the result

Question 2

Injective in other words

Answer 2

one-to-one

Question 3

Surjective in other words

Answer 3

onto

Question 4

Identity function

Answer 4

y equals x

Question 5

Reciprocal function

Answer 5

1 over x

Question 6

Inverse square function

Answer 6

1 over x squared

Question 7

What is the number in a logarithm called

Answer 7

argument

Question 8

Which transformations are rigid

Answer 8

translations, reflections and rotations

Question 9

Which transformations are non-rigid

Answer 9

stretches and shrinks

Question 10

Vieta’s formulas

Answer 10

sum of roots equals -b/a; product of roots equals c/a

Question 11

Fundamental theorem of algebra

Answer 11

every nonconstant polynomial has a complex root (therefore, every polynomal of degree at least 1 can be factored to linear factors)

Question 12

Polynomials theorem 1

Answer 12

integer root divides constant coefficient of a polynomial

Question 13

Polynomials theorem 2

Answer 13

polynomials have a root a / b, where a divides a0 and b divides an

Question 14

Degree of a polynomial root

Answer 14

how many times it appears

Question 15

Division theorem for polynomials

Answer 15

for dividing every polynomial by another polynomial there exist two other polynomials, so that one is a factor and the other the remainder

Question 16

Remainder theorem

Answer 16

remainder when dividing a polynomial by x - a is equal to p(a)

Question 17

Factor theorem

Answer 17

a polynomial has a factor (ax - b) iff p(b/a) equals 0

Question 18

Vieta’s formulas for general polynomials

Answer 18

sum of root equals -(an-1)/an; product of roots equals (a0/an)*(-1)**n

Question 19

Rational function

Answer 19

function of the form of the quotient of two polynomials

Question 20

When is a rational function in a reduced form

Answer 20

if both polynomials have no common factor

Question 21

What happens if we have a pole of an odd degree

Answer 21

graph will change sign

Question 22

Where does a rational function intersect an asymptote

Answer 22

at the roots of the remainder

Question 23

How is a curved asymptote called?

Answer 23

oblique asymptote

Question 24

When do we have to check the solution of an equation?

Answer 24

if we squared it at any point; we used the rules of logarithms

Question 25

What is half-life?

Answer 25

time it takes for a given amount of material to decrease to half of its original amount

Question 26

When does the inequality sign change?

Answer 26

if we put both sides as the exponent of a function with base < 1

Question 27

What is a statement?

Answer 27

A sentence that can be true or false

Question 28

What is an axiom?

Answer 28

an original statement, which we want to hold, to define more complex statements from it

Question 29

Which words tell you of implication?

Answer 29

if A then B
A implies B
from A follows b
A only if B

Question 30

Which words tell you of equivalence?

Answer 30

A iff B

A is equivalent to B

Question 31

What are antedecent and consequent?

Answer 31

in implication A is antedecent and B is consequent

Question 32

What is tautology?

Answer 32

a statement that is always true

Question 33

What is the contrapositive of ‘if P then Q’?

Answer 33

‘if not Q then not P’, they are equivalent

Question 34

What is the converse of ‘if P then Q’?

Answer 34

‘If Q then P’, they are not equivalent

Question 35

What is equivalence ‘P iff Q’ same as?

Answer 35

‘If P then Q’ and ‘If Q then P