APPC - Unit 2: Exponential and Logarithmic Functions Flashcards

Sequence

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

Arithmetic Sequence

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

Geometric Sequence

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

Linear Function

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

Exponential Function

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

Nth Term Formula (Arithmetic)

a_n = a₁ + d(n - 1)

Nth Term (Geometric)

a_n = a₁(r) ^n-1

Exponential Functions

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

General Form of an Exponential Function

the standard equation for an exponential function.

Additive Transformation of an Exponential Function

adding a constant to an exponential function.

Negative Exponent Property

the property of negative exponents in exponential functions.

Product Property

the property of multiplying exponential functions with the same base.

Power Property

the property of raising an exponential function to a power.

Inverse Functions

the inverse relationship between two functions.

Identity Function

a function that returns the same value as its input.

Inverse of Exponential Functions

the inverse relationship between exponential and logarithmic functions.

Logarithmic Functions

functions that model proportional growth or repeated multiplication.

Log Product Property

the property of multiplying logarithmic functions.

Log Quotient Property

the property of dividing logarithmic functions.

Log Exponential Property

the property of exponentiating logarithmic functions.

Natural Log Property

the property of logarithmic functions with base e.

Exponential and Logarithmic Equations and Inequalities

solving equations and inequalities involving exponential and logarithmic functions.

Semi-Log Plots

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

Linear Model for Semi-Log Plot

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

Horizontal Translation Left

f(x+h)

Horizontal Translation Right

f(x-h)

Horizontal Stretch/Shrink

f(kx)

Vertical Stretch/Shrink

kf(x)