Parent function

Definition

A parent function is the simplest form of a family of functions that preserves the shape and orientation of the graph. Examples include $y = e^x$ for exponential functions and $y = \log_b(x)$ for logarithmic functions.

5 Must Know Facts For Your Next Test

1. The parent function for logarithmic functions is $y = \log_b(x)$, where $b$ is the base.
2. The domain of the parent logarithmic function is $(0, \infty)$.
3. The range of the parent logarithmic function is $(-\infty, \infty)$.
4. The graph of a parent logarithmic function passes through the point (1,0).
5. For bases greater than one, the parent logarithmic function increases; for bases between zero and one, it decreases.

Review Questions

• What is the general form of a parent logarithmic function?
• What are the domain and range of a parent logarithmic function?
• Through which point does the graph of a parent logarithmic function always pass?

Related terms

Exponential Function: $y = b^x$, where $b$ is a positive real number not equal to one. The inverse is a logarithmic function.

Logarithm: The exponent to which a base must be raised to produce a given number, typically written as $\log_b(x)$.

$e$ (Euler's Number): $e \approx 2.71828$, an irrational constant often used as the base in natural logarithms.