Polynomial and Rational Functions Flashcard

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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: f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n ≠ 0.

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What is the degree of a polynomial?

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The degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial f(x) = 2x^3 + 3x^2 + 1, the degree is 3.

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What is a rational function?

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A rational function is a function that can be expressed as the quotient of two polynomials. It has the form f(x) = P(x)/Q(x), where P(x) and Q(x) are polynomials and Q(x) ≠ 0.

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What is a vertical asymptote?

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A vertical asymptote is a vertical line x = a where a rational function approaches infinity or negative infinity as x approaches a. It occurs where the denominator of the function is zero.

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What is a horizontal asymptote?

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A horizontal asymptote is a horizontal line y = b that a function approaches as x approaches infinity or negative infinity. It indicates the behavior of the function at extreme values of x.

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How do you find the vertical asymptote of a rational function?

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To find the vertical asymptote, set the denominator of the rational function equal to zero and solve for x.

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What is the leading coefficient of a polynomial?

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The leading coefficient is the coefficient of the term with the highest degree in a polynomial. For example, in f(x) = 4x^3 + 2x^2 + 5, the leading coefficient is 4.

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What does it mean for a polynomial to be classified as 'quadratic'?

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A polynomial is classified as quadratic if its degree is 2. The general form is f(x) = ax^2 + bx + c, where a ≠ 0.

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What is the difference between even and odd degree polynomials?

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Even degree polynomials have the same end behavior (both ends go up or both go down), while odd degree polynomials have opposite end behavior (one end goes up and the other goes down).

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What is a binomial?

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A binomial is a polynomial with exactly two terms. For example, f(x) = x^2 + 5 is a binomial.