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Parent function

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College Algebra

Definition

A parent function is the simplest form of a function in a family of functions that preserves the shape and general characteristics of the entire family. For logarithmic functions, the parent function is $f(x) = \log_b(x)$ where $b$ is the base of the logarithm.

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5 Must Know Facts For Your Next Test

  1. The most common bases for logarithmic functions are 10 (common logarithm) and e (natural logarithm).
  2. The graph of a basic logarithmic function has a vertical asymptote at $x = 0$.
  3. Logarithmic functions pass through the point $(1,0)$ regardless of their base.
  4. The domain of a parent logarithmic function $f(x) = \log_b(x)$ is $(0, \infty)$ while its range is $(-\infty, \infty)$.
  5. Transformations such as translations, reflections, and dilations can be applied to the parent function to obtain other members of its family.

Review Questions

  • What is the vertical asymptote for the parent logarithmic function?
  • Which point do all parent logarithmic functions pass through?
  • Describe how you would transform $f(x) = \log_2(x)$ to shift it up by 3 units.
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