Polynomial functions follow a specific formula where terms are in descending order by the exponent of x. All polynomial functions have zeros, which are the x-intercepts with opposite signs. Examples are provided of polynomial functions in standard form with positive, integer exponents like f(x) = 6x^4 - 3x^2 + 2x - 5. Non-polynomial functions do not follow these rules, such as having negative exponents or non-descending terms. Important properties of polynomial functions include the degree, leading coefficient, factored and standard forms.

1. Polynomial FunctionsGage GirtenB2

2. The Polynomial Function FormulaPolynomial functions fit into this formula…f(x) = ax^h + bx^h-1 + cx ^h-2 + … gx + hIn this, a, b, c …, g, h are real numbers, and are positive integers

3. Function RulesAll polynomial functions have zeros. The relationship between the x – intercepts and the zero are inversely proportional (opposite signs)Ex. y = x +5The zero if this graph is – 5Ex. y = (x + 6)(x – 5)The zeros are -6, and 5

4. Examples of Polynomial FunctionsPolynomial functions must be in descending order of the value of x’sExs….F(x) = 6x^4 – 3x^2 + 2x -5F(x) = x^7 – 2F(x) = x^12

5. Ex. continuedNon – Polynomial functionsF(x) = x^-2 +5 the exponent of a polynomial function must be positiveF(x) = 2x^1/2 + 3x^2 -4 the terms must be in descending order for it to be a polynomial fucntion

6. More Important InfoDegree – The highest value of x when the function is in standard fromLeading Co-efficient – the leading efficient of the first term, when the terms are in descending orderFactored Form – f(y) = (x – r1)(x – r2)(x – r3)Standard Form – f(y) = ax^2 = bx +c

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