AP Precalculus Review: Modeling with Exponential and Logarithmic Functions

Sequence

An ordered list of numbers where the domain is a subset of integers.

Arithmetic Sequence

A sequence where consecutive terms share a common difference.

Common Difference (d)

The fixed amount added to each term of an arithmetic sequence.

Geometric Sequence

A sequence where consecutive terms share a common ratio.

Common Ratio (r)

The constant factor multiplied to each term of a geometric sequence.

Linear Function

A function that has a constant rate of change.

Exponential Function

A function where the output changes by multiplying by a factor.

Additive Change

A change involving a constant difference between terms.

Multiplicative Change

A change involving a constant ratio between terms.

Growth Factor

The base (b) in an exponential function that indicates growth.

Decay Factor

The base (b) in an exponential function that indicates decay.

Exponential Growth

When the growth factor b is greater than 1.

Exponential Decay

When the growth factor b is between 0 and 1.

Limiting Behavior for Growth

As x approaches infinity, f(x) approaches infinity for growth.

Limiting Behavior for Decay

As x approaches infinity, f(x) approaches 0 for decay.

Concavity

The direction in which a graph curves; can be up or down.

Relative Maxima

The highest point in a local region of a function.

Relative Minima

The lowest point in a local region of a function.

Inflection Point

A point on the graph where the concavity changes.

Function Composition

Combining two functions such that the output of one becomes the input of the other.

Inverse Function

A function that reverses the mapping of the original function.

Logarithm

The exponent to which the base must be raised to yield a given number.

Product Rule of Logarithms

logb(xy) = logb(x) + log_b(y)