Final Exam Unit 1 and 2 Review

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What is a polynomial function?

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A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. The general form is p(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where n is a non-negative integer.

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How do you determine the intervals where a polynomial function is greater than or equal to zero?

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To determine the intervals where a polynomial function p(x) is greater than or equal to zero, perform a sign analysis. Find the roots of the polynomial, create a sign chart, and test intervals between the roots to see where the function is positive or zero.

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What is the equivalent form of the function h(x) = 100 * 9^x?

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The equivalent form is h(x) = 100 * 3^{2x}, since 9 can be expressed as 3^2.

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What is the least possible degree of a polynomial function g(x)?

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The least possible degree of a polynomial function is determined by the highest power of x in the polynomial. For example, if g(x) has a term like x^3, the least degree is 3.

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What does the end behavior of a polynomial function indicate?

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The end behavior of a polynomial function describes how the function behaves as x approaches positive or negative infinity. It is determined by the leading term of the polynomial.

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What is the significance of the leading coefficient in a polynomial function?

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The leading coefficient affects the end behavior of the polynomial. If it is positive and the degree is even, the function rises on both ends; if it is negative, it falls on both ends.

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How do you find the coefficient of a specific term in a polynomial expansion?

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To find the coefficient of a specific term in a polynomial expansion, use the binomial theorem or expand the polynomial and collect like terms.

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What is the binomial theorem?

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The binomial theorem provides a formula for expanding expressions of the form (a + b)^n. It states that (a + b)^n = Σ (n choose k) * a^(n-k) * b^k for k = 0 to n.

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What is a sign analysis chart?

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A sign analysis chart is a tool used to determine the sign (positive or negative) of a polynomial function over different intervals based on its roots.

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What is the difference between a polynomial and a rational function?

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A polynomial function is a sum of terms with non-negative integer exponents, while a rational function is a ratio of two polynomials.