## Graphing Polynomial Functions Review

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Limits Number value that f(x) approaches as the values of x approach a specific numberIf f(x) is a polynomial or a rational function and a is in the domain of f(x), then Limits that fail to exist 1. If f(x) approaches a different number from the right than from the left: 2. If f(x) increases or decreases without bound as it approaches a number: 3. If f(x) oscillates between 2 fixed value One-sided limits If only approaching from the right If only approaching from the left Limit Existence Theorem = L iff = L = Vertical Asymptote If = or = Then x=a is a vertical asymptote Horizontal Asymptote If or Then y=b is a horizontal asymptote

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THE LEGACY OF GREECE Culture Science &Technology Arts Government Ancient Olympics Invented water clock and water Organ. Sculptures. Consisted of many City States Utilized Slavery developed extensive silver mines Pottery (usually painted) Monarchy- Rule by a king (e.g. Corinth) Many wars (e.g. Trojan war) Considered questions of astronomy, mathematics, physics and biology. Theater ( Plays, dramas) Oligarchy-Rule by a small group. (e.g. Sparta) Believed in many gods. (Polytheistic) Aqueducts for water irrigation Architecture (Temples, Coliseums) Democracy-Rule by the citizens (e.g. Athens)

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By now, you should be familiar with variables and exponents, and you may have dealt with expressions like 3x4 or 6x. Polynomials are sums of these "variables and exponents" expressions. Each piece of the polynomial, each part that is being added, is called a "term". Polynomial terms have variables which are raised to whole-number exponents (or else the terms are just plain numbers); there are no square roots of variables, no fractional powers, and no variables in the denominator of any fractions. Here are some examples:Notice the exponents on the terms. The first term has an exponent of 2; the second term has an "understood" exponent of 1; and the last term doesn't have any variable at all.

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Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics.

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Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics.

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Factor x2 + 5x + 6.
I need to find factors of 6 that add up to 5. Since 6 can be written as the product of 2 and 3, and since 2 + 3 = 5, then I'll use 2 and 3. I know from multiplying polynomials that this quadratic is formed from multiplying two factors of the form "(x + m)(x + n)", for some numbers m and n. So I'll draw my parentheses, with an "x" in the front of each:
(x )(x )
Then I'll write in the two numbers that I found above:
(x + 2)(x + 3)
This is the answer: x2 + 5x + 6 = (x + 2)(x + 3)

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