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Graphs of Logarithmic Functions

Explore College Algebra concepts with a focus on graphs of logarithmic functions. Learn how to identify the domain, understand transformations, and interpret key features of logarithmic graphs. Ideal for students and educators alike.

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College AlgebraGraphs of Logarithmic FunctionsIdentify the domain of a logarithmic functionBefore working with graphs, we will take a look at the domain (the set of input values) for which the logarithmic function is defined.Recall that the exponential function is defined asy - bxfor any real numberx and constantb >01, whereThe domain ofyis(-OO, 00)The range ofy is(0,co)In the last section we learned that the logarithmic functiony ~loga( z )is the inverse of the exponential functiony - bx. So, as inverse functions:The domain ofy ~fa)is the range ofy ~bT( 0 , 0 0 )The range ofy ~l o g U ® )is the domain ofy ~bx( — 0 0 , 0 0 )
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