Exponential and Logarithmic Functions
MA, Stanford University
Teaching in the San Francisco Bay Area
Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts
All exponential decay functions, that is, if 0 < b < 1 , will have the same general shape and asymptotes as the parent function. To graph quickly, use rules of transformations. A number added or subtracted to x in the exponent will represent a horizontal shift, and a number added or subtracted to the exponential term will be a vertical shift. A number multiplied by the exponential term will cause a vertical stretch or compression, and if negative, will reflect the graph across the x axis. Don't forget to apply the horizontal and vertical shifts to the asymptote, as well! Verify your graph by plugging in an x,y pair. Remember that not all fractional bases represent decay- only those where 0 < b < 1.
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