Horizontal: Affect the x-values, inside the function. | Vertical: Affect the y-values, outside the function.

Growth: Base > 1, function increases as x increases. | Decay: 0 < Base < 1, function decreases as x increases.

Product: Adding exponents when multiplying same bases. | Power: Multiplying exponents when raising a power to a power.

$b^x$: Exponential growth if b > 1, decay if 0 < b < 1. | $b^{-x}$: Exponential decay if b > 1, growth if 0 < b < 1.

Horizontal translation: Shifts the graph left or right. | Vertical stretch: Changes the steepness of the graph.

Horizontal: Affects the x-axis, compression or stretch. | Vertical: Affects the y-axis, stretch or compression.

$f(x) = b^{x+k}$: Horizontal shift. | $f(x) = b^x + k$: Vertical shift.

$f(x) = b^{cx}$: Horizontal dilation. | $f(x) = cb^x$: Vertical dilation.

x-axis: Changes the sign of the output. | y-axis: Changes the sign of the input.

$b^{1/2}$: Square root of b. | $(b)^{2}$: Square of b.

A function of the form $f(x) = ab^x$, where $a$ is a constant, $b$ is the base, and $x$ is the exponent.

The base, $b$, is a positive real number not equal to 1 in the exponential function $f(x) = ab^x$.

A shift of a function's graph left or right along the x-axis.

A stretch or compression of a function's graph in the vertical direction (y-axis).

A stretch or compression of a function's graph in the horizontal direction (x-axis).

An exponent that indicates the reciprocal of the base raised to the positive value of the exponent.

An exponent in the form of 1/n, representing the nth root of the base.

The reciprocal of a number x is 1/x.

A transformation where the graph of a function is flipped over the y-axis.

A change in the position, shape, or size of a function's graph.

$b^m * b^n = b^{m+n}$

$(b^m)^n = b^{mn}$

$b^{-n} = \frac{1}{b^n}$

$b^{\frac{1}{k}} = \sqrt[k]{b}$

$f(x+k)$

$f(x-k)$

$a*f(x)$

$f(cx)$

$f(-x)$

$-f(x)$