2.11

Logarithmic Functions

about 30 min · 5 short parts · stop after any part
Every log graph has the same skeleton: a wall (asymptote), the point (1,0)(1,0), and a slow climb.
By the end you can read domain, range, asymptote and end behavior straight from the formula.

The path

  1. 1
    The parent log graph
    You can list the key features of y=log⁡bxy = \log_b x.
  2. 2
    Moving the graph
    You can sketch alog⁡b(x−h)+ka\log_b(x-h)+k by moving the parent.
  3. 3
    Asymptote, domain, range
    You can find the wall and domain from the inside of the log.
  4. 4
    End behavior
    You can write both limits for a log function.
  5. 5
    Calculator special cases
    You can handle ln⁡∣x−h∣\ln|x-h|, a fraction inside, and two logs compared.