San Diego City College - Math 46: Elementary Algebra And Geometry

Front 1

The domain of a function, f, is

Back 1

The set of all the correct, or allowed, input values to the function.

Front 2

The set of all allowed inputs for a function is called the...

Back 2

Domain

Front 3

The set of all output values of a function is called the...

Back 3

Range

Front 4

Every function is a relation, but not every relation is a...

Back 4

Function

Front 5

Associates corresponding numbers from two sets, but is not necessarily a function

Back 5

Relation

Front 6

When a relation is not a function...

Back 6

For a given number in the Domain, more than one value from the Range is associated with it.

Front 7

When I make a graph of a relation on the x-y plane, and i can draw a vertical line that intersects the graph in more than one place...

Back 7

The graph is not that of a function. (Vertical Line Test)

Front 8

A collection of values is called a...

Back 8

Set

Front 9

To write a set...

Back 9

Write a comma-separated list of numbers, and enclose in curly braces.

Front 10

Example of a finite set, A, containing numbers

Back 10

A = { 1, 2, 3, 4, 5, 6, 7, 8, 9 }

Front 11

Set-builder notation process

Back 11

Put a curly brace, what you want in your set, a vertical bar (|), and a criteria that says what belongs in the set

Front 12

Set-builder notation for all x's except those less than four

Back 12

{ x | x >= 4 }

Front 13

The Natural Numbers, N

Back 13

N = {1, 2, 3, 4, 5, 6, 7, ... }

Front 14

The Integers, Z

Back 14

Z = { ... , -3, -2, -1, 0, 1, 2, 3, ... }

Negative and positive counting numbers and zero.

Front 15

Another name for The Natural Numbers

Back 15

The "counting numbers"

Front 16

What belongs in The Natural Numbers?

Back 16

Positive, whole numbers, starting with 1

Front 17

What belongs in The Integers?

Back 17

Positive and negative whole numbers, and zero.

Front 18

The Rational Numbers, Q

Back 18

The set of all numbers that can be expressed as the quotient of two integers.

Front 19

The bar in a fraction means what operation?

Back 19

Division, or "divided by."

Front 20

Set-builder notation for The Rational Numbers

Back 20

Q = { x | x = p/q, p,q \elt Z, q \ne 0 }

Front 21

Why can't the bottom of a fraction be zero?

Back 21

Because dividing by zero is not allowed.

Front 22

What belongs in The Rational Numbers?

Back 22

Positive and negative whole numbers and fractions composed of only integer top and bottom, and zero.

Front 23

The Real Numbers, R

Back 23

All of the numbers, including irrational numbers such as e and \pi, including N, Z, and Q

Front 24

All of the counting numbers

Back 24

The Natural Numbers, N

Front 25

All of the positive and negative whole numbers, including zero

Back 25

The Integers, Z

Front 26

All of the fractions where the top and bottoms are integers, and the bottom is never zero.

Back 26

The Rational Numbers, Q

Front 27

All of the numbers, including all the members of N, Z, and Q, as well as irrational numbers, such as e and \pi

Back 27

The Real Numbers, R

Front 28

Takes something out of another set

Back 28

Set Subtraction

Front 29

Gives you all the values in both sets, including any values they have in common.

Back 29

Union

Front 30

Gives you only the values that two different sets have in common

Back 30

Intersection

Front 31

Used for "no solution" answers, this set contains nothing, i.e., no values. Also written as { }.

Back 31

The Empty Set

Front 32

Contains everything in all the sets you're working with, plus everything else.

Back 32

The Universe

Front 33

All the values that are not in a set, A.

Back 33

The Compliment, A-tilde.

Front 34

A function that is a fraction with formulas on top and bottom

Back 34

Rational Function, f(x) = p(x) / q(x), q(x) \ne 0

Front 35

How to find the domain of a rational function

Back 35

Start with The Real Numbers. Exclude all values of x that make the bottom equal zero, or any expressions under radicals in the top negative.

Front 36

This is the set-builder notation for all real numbers except zero.

Back 36

{x \elt R | x \ne 0 }

Front 37

This is the set-builder notation for all rational numbers between 2 and 3, including both 2 and 3.

Back 37

{ x \elt Q | 2 \lte x \lte 3 }

Front 38

How to express that a value, x, is in between and including, a pair of values

Back 38

Sandwich x in between two less-than-or-equal-to symbols, and the particular numbers, in order.

Front 39

This is the set-builder notation for all the integers bigger than 5.

Back 39

{ x \elt Z | x > 5 }

Front 40

To evaluate a function, f, at a particular value of x, means do this.

Back 40

Plug the particular value of x into the function's formula and then get the answer.

Front 41

Distributive Property

Back 41

a(b + c) = ab + ac

Front 42

a(b + c) = ab + ac

Back 42

Distributive Property

Front 43

Commutative Property of Addition

Back 43

a + b = b + a

Front 44

a + b = a + b

Back 44

Commutative property of addition; that is, you can add in any order.

Front 45

Anti-Commutative Property of Subtraction

Back 45

b - a = (-1)(a - b)

Front 46

b - a = (-1)(a - b)

Back 46

Anti-commutative property of subtraction; means, that if I flip the order of subtraction, then a factor of minus one comes flying out in front. Also, if I take a difference and multiply it by minus one, the order of subtraction will flip.

Front 47

a - b = (-1)(b - a)

Back 47

Anti-commutative property of subtraction; means, that if I flip the order of subtraction, then a factor of minus one comes flying out in front. Also, if I take a difference and multiply it by minus one, the order of subtraction will flip.

Front 48

Anti-Commutative Property of Subtraction

Back 48

a - b = (-1)(b - a)

Front 49

Commutative Property of Multiplication

Back 49

a x b = b x a

Front 50

a x b = b x a

Back 50

Commutative Property of Multiplication

Front 51

Additive Identity

Back 51

a + 0 = 0 + a = a

Front 52

0 + a = a + 0 = a

Back 52

Additive identity; meaning, zero is the one number I can add to any other number, and in any order, and I get back the same number I started with.

Front 53

Multiplicative Identity

Back 53

a x 1 = 1 x a = a

Front 54

1 x a = a x 1 = a

Back 54

Multiplicative identity; meaning, 1 is the only number I can multiply times any other number and I get back the number I started with.

Front 55

Adding a number and its opposite together give this.

Back 55

a + (-a) = 0

Front 56

a + (-a) = 0

Back 56

Adding a number to its own opposite, or subtracting two equal numbers, gives zero as the answer.

Front 57

a - a = 0

Back 57

Adding a number to its own opposite, or subtracting two equal numbers, gives zero as the answer.

Front 58

If x - 2y = 0, then...

Back 58

x = 2y by the fact that two things subtracted and giving me zero as the answer, are indeed equal to each other.