College Algebra – Exam #1 Review – Flashcards
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Natural Numbers (Counting Numbers)
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1, 2, 3, 4, 5, 6, 7, 8, 9, etc. Whole numbers that are not negative.
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Integers
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-3, -2, -1, 0, 1, 2, 3, etc. These are the natural numbers, their additive inverses (negatives), and 0.
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Rational Numbers
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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.
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Irrational Numbers
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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.
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Real Numbers
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2, -10, -131.3337, 1/3, etc. Real Numbers can be represented by decimal numbers. Real numbers include both the rational and irrational numbers.
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Order of Operations is...
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PEMDAS Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction.
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Example: a/0
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Not defined.
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Example: 0/a
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0.
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What does Relation mean?
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A relation is a set of ordered pairs.
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What is an Ordered Pair?
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(x, y)
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What is the Domain?
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x.
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What is the Range?
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y.
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What must you ALWAYS be careful with?
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Your signs! Be very careful with your NEGATIVE signs. example {4x-2(x+3)} Remember to distribute the negative in front of the 2. Answer: 4x-2x-3= 2x-3
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Absolute Value is...
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ALWAYS POSITIVE
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What is Function Notation?
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f(x)=y
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What is a Function?
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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).
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What is the Domain of a Function?
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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.
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What is the Range of a Function?
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The Range of a Function f(x) is the set {y=f(x)}.
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What is the Vertical Line Test?
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If every vertical line intersects a graph at no more than one point, then the graph represents a function.
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How do we read? And how should I read a graph?
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From left to right. Read a graph the same way.
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What is the U (Union) Symbol?
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Joins two pairs. You write this in between the inequality of the interval notation.
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What is the Slope-Intercept Form of an Equation of a Line?
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Also known as a Linear Function.
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With Verticle Lines...
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The Slope is undefined!
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What is an Equation?
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An Equation is a statement that two mathematical expressions are equal.
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linear Inequalites
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*Keep all X's to the left of the equation. *When we multiply or divide by a negative number reverse the inequality sign.
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Principles of Inequalites
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a0 then ac;bc a;b and cbc
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10x-3;5x+2
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x;5
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Try This: 7x+14=12x+4
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x=2
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7(x-5)=6(x-2)
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x=47
