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What is the definition of an oblique asymptote?

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An oblique asymptote is a slanting line that a graph approaches as the input values (x) go to positive or negative infinity. It occurs when the degree of the numerator is one higher 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 of a rational function, perform polynomial long division. The quotient (ignoring the remainder) will give you the equation of the oblique asymptote.

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What does it mean for a function to be greater than zero, f(x) > 0?

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It means that the output values of the function are positive. This occurs in the intervals where the graph of the function lies above the x-axis.

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What is the significance of the intervals in which f(x) > 0?

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The intervals where f(x) > 0 indicate the values of x for which the function produces positive outputs, which can be important for understanding the behavior of the function.

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What is the difference between closed and open intervals?

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A closed interval includes its endpoints (e.g., [a, b]), while an open interval does not include its endpoints (e.g., (a, b)).

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What is the formula for finding the vertical asymptote of a rational function?

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The vertical asymptote occurs at the values of x that make the denominator equal to zero, provided that these values do not also make the numerator zero.

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What is the definition of a rational function?

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What is the horizontal asymptote of a rational function?

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The horizontal asymptote is a horizontal line that the graph of the function approaches as x approaches positive or negative infinity. It is determined by the degrees of the numerator and denominator.

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How do you determine the horizontal asymptote of a rational function?

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1. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y=0. 2. If the degrees are equal, the horizontal asymptote is y = leading coefficient of numerator / leading coefficient of denominator. 3. If the degree of the numerator is greater, there is no horizontal asymptote.