1. Set g(x) > 0. 2. Solve for x. This gives the domain of f(x).

Rewrite the equation in exponential form: $x = b^c$.

1. Identify the vertical asymptote at x = h. 2. Plot a few key points. 3. Sketch the curve, considering the base 'b' and the vertical stretch 'a'.

Consider the base 'b'. If b > 1, y approaches negative infinity. If 0 < b < 1, y approaches positive infinity.

Consider the base 'b'. If b > 1, y approaches positive infinity. If 0 < b < 1, y approaches negative infinity.

1. Combine logarithms using properties. 2. Convert to exponential form. 3. Solve for x. 4. Check for extraneous solutions.

1. Replace f(x) with y. 2. Swap x and y. 3. Solve for y. 4. Replace y with $f^{-1}(x)$.

Apply transformations in the correct order: horizontal shifts, stretches/compressions, reflections, and vertical shifts.

Substitute the solution back into the original equation and ensure the argument of each logarithm is positive.

Set y = 0 and solve for x.

The inverse of an exponential function; 'undoes' exponentiation.

x > 0 (positive real numbers)

All real numbers

A vertical line that the graph of a function approaches but never touches.

The value inside the logarithm, e.g., 'x' in $\log_b(x)$. Must be positive.

The value 'b' in $\log_b(x)$. Determines if the function is increasing or decreasing.

Describes the curve's shape: either concave up or concave down, but not both.

A transformation of a graph where the entire graph is moved left or right.

Describes how the function behaves as x approaches positive or negative infinity.

Changes to a function's graph, such as shifts, stretches, or reflections.

$y = \log_b(x)$

$\lim_{x \to 0^+} a\log_b(x) = \pm \infty$

$\lim_{x \to \infty} a\log_b(x) = \pm \infty$

$g(x) = \log_b(x + k)$

$b^y = x$

$\log_b(1) = 0$

$\log_b(b) = 1$

$\log_a(x) = \frac{\log_b(x)}{\log_b(a)}$

$\log_b(MN) = \log_b(M) + \log_b(N)$

$\log_b(\frac{M}{N}) = \log_b(M) - \log_b(N)$