Polynomial Functions and Rational Functions Test 2

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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 a rational function?

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A rational function is a function that can be expressed as the quotient of two polynomials. The general form is: f(x) = P(x)/Q(x), where P(x) and Q(x) are polynomials and Q(x) ≠ 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 4x^3 + 2x^2 - x + 7, the degree is 3.

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What are vertical asymptotes?

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Vertical asymptotes are lines x = a where a rational function approaches infinity or negative infinity as x approaches a. They occur where the denominator of the function is zero.

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How do you find vertical asymptotes of a rational function?

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

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What is an oblique asymptote?

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An oblique asymptote (or slant asymptote) occurs when the degree of the numerator is one greater than the degree of the denominator in a rational function.

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

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To find the oblique asymptote, perform polynomial long division on the rational function. The quotient (without the remainder) gives the equation of the oblique asymptote.

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What is the standard form of a polynomial?

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The standard form of a polynomial is written in descending order of the degree of its terms. For example, 3x^4 - 2x^3 + x - 5 is in standard form.

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What is a transformation in the context of polynomial functions?

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A transformation refers to changes made to the graph of a function, such as shifts, stretches, compressions, or reflections.

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What does a vertical stretch of a function mean?

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A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller.