College Algebra (Math 1111) - Exam #1 Review

Real Numbers

2, -10, -131.3337, 1/3, etc.

Real Numbers can be represented by decimal numbers. Real numbers include both the rational and irrational numbers.

Natural Numbers (Counting Numbers)

1, 2, 3, 4, 5, 6, 7, 8, 9, etc.

Whole numbers that are not negative.

Integers

-3, -2, -1, 0, 1, 2, 3, etc.

These are the natural numbers, their additive inverses (negatives), and 0.

Rational Numbers

2/1, 1/3, (-1/4), 22/7, 0, 1.2, etc.

Every integer is a rational number. Rational numbers can be expressed as decimals that either terminate (end) or repeat a sequence of digits.

Irrational Numbers

Irrational Numbers are numbers which are no rational numbers. They cannot be expressed as the ratio of two integers and has a decimal representation that does not terminate or repeat.

Classify: 5

Natural Number, Integer, Rational Number.

Classify: -1.2

Rational Number.

Classify: 13/7

Rational Number

Order of Operations is...

PEMDAS

Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction.

Example: a/0

Not defined.

Example: 0/a

0.

What is Mean?

The quotient of the sum of several quantities and their number; an average.

What is Median?

The median (middle) value of a range of values.

What is a Cartesian (rectangular) coordinate plane?

What does Relation mean?

A relation is a set of ordered pairs.

What is an Ordered Pair?

(x, y)

What is the Domain?

x.

What is the Range?

y.

What is the Distance Formula?

What is the Midpoint Formula?

What is the Standard Equation of a Circle?

What is a Circle?

A Circle is a collection/set of points that are on a fixed distance (radius) from a fixed point (center).

What must you ALWAYS be careful with?

Your signs!

Absolute Value is...

Absolute Value is the distance from zero; always positive.

What is Function Notation?

f(x)=y

What is a Function?

A Function is a relation in which every element in a first set (domain) is paired to a unique element on a second set (range).

What is the Domain of a Function?

The Domain of a Function is the set of values that makes the function well defined. If the function is not well defined at a point, then that point is not in the domain.

What is the Range of a Function?

The Range of a Function f(x) is the set {y=f(x)}.

What is the Vertical Line Test?

If every vertical line intersects a graph at no more than one point, then the graph represents a function.

Increasing & Decreasing Functions

f increases on l if, whenever x^1

What are the "Library of Functions?"

How do we read? And how should I read a graph?

From left to right. Read a graph the same way.

What is Interval Notation and how do you use it?

What is the U (Union) Symbol?

Joins two pairs. You write this in between the inequality of the interval notation.

What is the Average Rate of Change?

The Average Rate of Change of f from x^1 to x^2 is...

y^2-y^1/x^2-x^1

What is the Difference Quotient?

What is the Point-Slope Form of an Equation of a Line?

What is the Slope Formula?

What is the Slope-Intercept Form of an Equation of a Line?

Also known as a Linear Function.

What is the Standard Form?

With Verticle Lines...

The Slope is undefined!

The General Form of the Equation of a Line is...

What is an Equation?

An Equation is a statement that two mathematical expressions are equal.

What are the three types of Equations?

1. Contradiction - No solution.

2. Identity - There is a solution.

3. Conditional - Satisfied by some, but not by all values of the variable.

What is a Linear Equation?

A Linear Equation in one variable is an equation that can be written in the form ax+b=0.

It must be equal to 1 (variable). It can not be squared or cubed unless they cancel out. Some may not even have variables, which it then is undefined.

What are the Properties of Equality?

How do you do Intersection-of-Graph method on a Calculator?

Type in your results using Y=, Graph and then hit 2nd>Calc and Intersect to find the Intersection. Can also be done by hand.

How do you Solve Application Problems?

What is the Formula when dealing with Distance, Speed, Time, etc.?

What are the Inequality Symbols?

What is Set Builder Notation?

What is a Compound Inequality?

Make sure to isolate the variable in between.

The solution set (in interval notation) of a compound inequality is always an interval of these: (a,b), [a,b], (a,b], [a,b).

What is the Absolute Value Function?

It is V-Shaped and is represented by y=|x|. It cannot be represented by single linear function.

What is the basic Absolute Value Equation?

You can also have a number inside, such as |x-3| and the equal sign can be changed to something such as < or >.