Week 1.

Question 1

Set

Answer 1

Group of Elements notated {element 1, …}

Question 2

∈

Answer 2

Element Belongs to a Set

Question 3

∉

Answer 3

Element doesn’t belong to a set

Question 4

⊆

Answer 4

Subset relationship

Question 5

or :

Answer 5

Such that

Question 6

Special-Sets

Answer 6

Sets of numbers that have their own special symbols

Question 7

N

Answer 7

Set of Natural numbers {1,2,3, …}

Question 8

Z

Answer 8

Set of Integer Numbers (whole number)

Question 9

Q

Answer 9

Set of ratio numbers p/q where p,q ∈ Z

Question 10

R

Answer 10

Most important. The set of all real numbers

Question 11

0

Answer 11

Empty set {}

Question 12

Union U

Answer 12

The set that contains all elements of 2 sets

Question 13

Intersection n

Answer 13

The set that contains all elements which are in both sets

Question 14

Exclusion

Answer 14

The set that contains all elements in one set that aren’t in the other A/B

Question 15

Interval

Answer 15

The set containing all real numbers between two bounds a,b where a,b ∈ R. Can be closed or open

Question 16

Closed Interval

Answer 16

Set contains the bounds of the interval [a,b]

Question 17

Open Interval

Answer 17

Set excludes the bounds of the interval (a,b)

Question 18

Infinity & Intervals

Answer 18

Infinity and -Infinity are concepts not real numbers, so shouldn’t be included in an interval set. Therefore, any interval containing -infinity, infinity will be open on the infinity side.

Question 19

Function

Answer 19

Consists of a domain (set A), a co-domain (Set B), and a rule that sends and element x in the domain to exactly one element in the co-domain f(x). There maybe cases where the rule doesn’t map to any elements in the co-domain

Question 20

Vertical Line test

Answer 20

Test if a rule is a function by graphing it, if a vertical line put through it intersects it at 2 or more times at any point it isn’t a function.

Question 21

Range

Answer 21

Set of all elements that a fucntion will actually output (lowest output, highest output)

Question 22

Combining functions

Answer 22

Functions can be added, subtracted, multiplied, or divided

Question 23

Composition function

Answer 23

X’s or variables in function f(x) replaced with another function g(x). Notated f(g(x)).

Question 24

Piecewise functions

Answer 24

different rules applied to different areas of the domain of the function

Question 25

Absolute function

Answer 25

a special case of a piecewise function where the function is reflected at the X intercept.

Question 26

e^x

Answer 26

the function has Yint =1 and a horizontal asymptote at y=0. domain = R and co-domain = R, range = [0, infinity)

Question 27

lnX

Answer 27

The function has Xint = 1 and a vertical asymptote of at x=0. Domain = (0, infinity), co-domain and range = R

Question 28

logarithmic rules

Answer 28

LogaB = LogcB/LogcA allows the base to be changed to c and simplify logarithmic functions.