Math 3 Unit 3 Flashcard 1 Polynomials

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What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, f(x) = 2x^3 - 4x^2 + 3x - 5 is a polynomial.

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What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial 4x^5 - 3x^2 + 2, the degree is 5.

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What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches positive or negative infinity.

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What is a vertical asymptote?

Back

A vertical asymptote is a vertical line x = a where the function approaches infinity or negative infinity as x approaches a.

Front

How do you find horizontal asymptotes for rational functions?

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For rational functions, compare the degrees of the numerator and denominator: If the degree of the numerator is less than the degree of the denominator, y = 0 is the horizontal asymptote. If they are equal, divide the leading coefficients.

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What does it mean for a function to be even?

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A function f(x) is even if f(-x) = f(x) for all x in the domain. Its graph is symmetric about the y-axis.

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What does it mean for a function to be odd?

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A function f(x) is odd if f(-x) = -f(x) for all x in the domain. Its graph is symmetric about the origin.

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

Back

The leading coefficient of a polynomial determines the end behavior of the graph. If it is positive, the graph rises to the right; if negative, it falls to the right.

Front

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

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

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What is the factor theorem?

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The factor theorem states that if f(c) = 0 for a polynomial f(x), then (x - c) is a factor of f(x).