Arithmetic: Constant difference, linear growth | Geometric: Constant ratio, exponential growth

Growth: b > 1, increasing function | Decay: 0 < b < 1, decreasing function

Exponential: Rapid growth/decay, horizontal asymptote | Logarithmic: Slow growth, vertical asymptote

$f^{-1}(x)$: Inverse function | $\frac{1}{f(x)}$: Reciprocal of the function

Linear: Equal intervals represent equal changes | Logarithmic: Equal intervals represent equal proportional changes

Composite: Combining functions sequentially | Inverse: Undoing a function

Exponential: Domain: all reals, Range: positive reals | Logarithmic: Domain: positive reals, Range: all reals

Exponential: Isolate, take logarithm | Logarithmic: Isolate, convert to exponential

Exponential: Horizontal asymptote, rapid growth/decay | Logarithmic: Vertical asymptote, slow growth

Exponential: Larger base = faster growth/decay | Logarithmic: Base influences steepness and position

It indicates exponential growth, where the rate of increase accelerates over time.

It indicates exponential decay, where the rate of decrease slows down over time.

It shows a slow rate of increase, approaching a vertical asymptote.

A larger base results in faster growth or decay.

The base affects the steepness and position of the graph relative to the y-axis.

A straight line, indicating a constant rate of growth or decay on a logarithmic scale.

Look for rapid growth or decay and a horizontal asymptote.

Look for a slow rate of increase and a vertical asymptote.

The initial value of the function.

The value for which the argument of the logarithm is equal to 1.

A function of the form $f(x) = ab^x$, where a and b are constants, and b > 0 and not equal to 1.

A function of the form $f(x) = \log_b(x)$, which is the inverse of an exponential function.

A sequence where each term differs by a constant amount (common difference).

A sequence where each term is multiplied by a constant amount (common ratio).

A function formed by combining two or more functions, where the output of one function becomes the input of another.

Functions that 'undo' each other. If $f(g(x)) = x$ and $g(f(x)) = x$, then $f(x)$ and $g(x)$ are inverses.

A graph that uses a logarithmic scale on one axis and a linear scale on the other.

The constant amount added to each term to get the next term.

The constant amount multiplied by each term to get the next term.

The value of the function when x = 0 (the 'a' in $f(x) = ab^x$).