Pre-Calculus Semester Exam Review

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What is an oblique asymptote?

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An oblique asymptote is a slanting line that a graph approaches as x approaches infinity 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, perform polynomial long division on the rational function. The quotient (ignoring the remainder) will give you the equation of the oblique asymptote.

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What is the logarithmic equation log₂(x + 5) = 3 asking for?

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This equation is asking for the value of x that makes the logarithm equal to 3, which means x + 5 = 2^3, or x + 5 = 8, leading to x = 3.

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What is a relative maximum in a function?

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A relative maximum is a point on the graph of a function where the function value is higher than the values of the function at nearby points. It indicates a peak in the graph.

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How can you determine the number of relative maximums in a function?

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You can determine the number of relative maximums by analyzing the first derivative of the function. Points where the first derivative changes from positive to negative indicate relative maximums.

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What is the result of adding complex numbers (5-2i) + (-7+8i)?

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The result is -2 + 6i. Combine the real parts (5 - 7) and the imaginary parts (-2i + 8i).

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What is the definition of a function?

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A function is a relation that assigns exactly one output for each input from its domain.

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

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A rational function is a ratio of two polynomials, while a polynomial function is a sum of terms consisting of variables raised to non-negative integer powers.

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What is the significance of the degree of a polynomial?

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The degree of a polynomial indicates the highest power of the variable in the polynomial, which affects the shape and behavior of its graph.

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What is the vertical line test?

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The vertical line test is a method to determine if a curve is a function. If any vertical line intersects the curve more than once, the curve is not a function.