AP Precalculus- Unit 2: Exponential and Logarithmic Functions Flashcards

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25 Terms

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Sequence

an ordered list of numbers, with each listed number being a term. It could be finite or infinite.

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Arithmetic Sequence

when each successive term in a sequence has a common difference (constant rate of change).

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Geometric Sequence

when each successive term in a sequence has a common ratio (consistent proportional change).

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Linear Function

if the output values of a function change at a constant rate.

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Exponential Function

if the output values of a function change at a proportional rate.

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Nth Term (Arithmetic)

the formula to find the nth term in an arithmetic sequence.

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Nth Term (Geometric)

the formula to find the nth term in a geometric sequence.

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Exponential Functions

always increasing or always decreasing, with no extrema or inflection points.

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Horizontal Translation/Vertical Dilation

shifting or scaling an exponential function.

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General Form of an Exponential Function

the standard equation for an exponential function.

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Additive Transformation of an Exponential Function

adding a constant to an exponential function.

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Negative Exponent Property

the property of negative exponents in exponential functions.

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Product Property

the property of multiplying exponential functions with the same base.

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Power Property

the property of raising an exponential function to a power.

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Inverse Functions

the inverse relationship between two functions.

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Identity Function

a function that returns the same value as its input.

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Inverse of Exponential Functions

the inverse relationship between exponential and logarithmic functions.

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Logarithmic Functions

functions that model proportional growth or repeated multiplication.

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Log Product Property

the property of multiplying logarithmic functions.

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Log Quotient Property

the property of dividing logarithmic functions.

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Log Exponential Property

the property of exponentiating logarithmic functions.

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Natural Log Property

the property of logarithmic functions with base e.

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Exponential and Logarithmic Equations and Inequalities

solving equations and inequalities involving exponential and logarithmic functions.

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Semi-Log Plots

plots with logarithmic scaling on the y-axis and linear scaling on the x-axis.

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Linear Model for Semi-Log Plot

the equation for a linear model on a semi-log plot.