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Overview
Pre-Calculus 12
Relations and Functions
15. Graph and analyze exponential and logarithmic functions
15.5 Graphing transformations of logarithmic functions
Graphing Transformations of Logarithmic Functions
See how shifts, stretches, and reflections move the graph of a logarithmic function, and practice sketching transformed logs step by step.
What You'll Learn
Every transformation of a logarithmic function follows the same rules used for other parent functions, applied to shifts, stretches, and reflections.
The vertical asymptote of the parent graph \(x = 0\) moves left or right only when the input variable itself is shifted.
Vertical shifts, stretches, and reflections change the shape or position of the curve but never move the vertical asymptote.
Because logarithmic functions are one to one, every transformed log graph still passes the horizontal line test.
Plotting two or three key points after finding the new asymptote is the fastest way to sketch an accurate graph.
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NS Curriculum Aligned