Parent function

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.

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.

Related terms

Exponential Function: A mathematical function in which an independent variable appears in the exponent. The general form is $f(x) = b^x$ where $b$ is a positive constant.

Asymptote: A line that a graph approaches but never touches or crosses.

$e$ (Euler's Number): $e$ is an irrational number approximately equal to 2.71828 and serves as the base for natural logarithms.