College Algebra Final Exam Review Part 3

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What are vertical asymptotes?

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Vertical asymptotes are lines x = a where a function approaches infinity or negative infinity as x approaches a. They occur where the function is undefined.

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What are horizontal asymptotes?

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Horizontal asymptotes are lines y = b that a function approaches as x approaches infinity or negative infinity. They indicate the behavior of the function at extreme values.

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How do you find vertical asymptotes of a rational function?

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Set the denominator equal to zero and solve for x. The values of x that make the denominator zero are the vertical asymptotes.

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How do you find horizontal asymptotes of a rational function?

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Compare the degrees of the numerator and denominator: If degree of numerator < degree of denominator, y = 0; if equal, y = leading coefficient of numerator/leading coefficient of denominator; if greater, no horizontal asymptote.

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What is a polynomial function?

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A polynomial function is a function that can be expressed in the form f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants and n is a non-negative integer.

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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 x in the polynomial expression.

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What are zeros of a polynomial?

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Zeros of a polynomial are the values of x for which the polynomial equals zero. They are also known as roots.

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How do you solve an exponential equation?

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To solve an exponential equation, take the logarithm of both sides, then use properties of logarithms to isolate the variable.

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What is the change of base formula for logarithms?

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What is the definition of a logarithm?

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