Parent function
from class: 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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Predict what's on your test 5 Must Know Facts For Your Next Test The most common bases for logarithmic functions are 10 (common logarithm) and e (natural logarithm). The graph of a basic logarithmic function has a vertical asymptote at $x = 0$. Logarithmic functions pass through the point $(1,0)$ regardless of their base. The domain of a parent logarithmic function $f(x) = \log_b(x)$ is $(0, \infty)$ while its range is $(-\infty, \infty)$. 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. "Parent function" also found in:
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