Logarithmic Functions & Graphing
Master domain and range, vertical asymptotes, graph transformations, key anchor points, and inverse relationships of logarithmic functions.
Key Concepts Covered:
- Domain & Vertical Asymptotes: For $f(x) = \log_b(x - h) + k$, set argument $x - h > 0$ to find domain $(h, \infty)$ and asymptote at $x = h$.
- Key Anchor Points: Base graphs $y = \log_b(x)$ pass through $(1, 0)$, $(b, 1)$, and $(1/b, -1)$.
- Transformations: Shifts $h$ units horizontally and $k$ units vertically; reflections across axes.
- Inverses & Symmetry: Logarithmic functions $y = \log_b(x)$ are reflections of exponential functions $y = b^x$ across $y = x$.