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Exponential Functions and their Graphs - Problem 6
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When we're asked to describe a transformation from f(x) to g(x), we first need to decide what values have remained the same and what have changed. Anything that has changed will represent some sort of change in the graph that we'll need to describe in words. A number added or subtracted inside the exponent represents a change in x, or the horizontal placement, and a number added or subtracted outside the exponential term represents a change in y, or a vertical shift. A value multiplied by the exponential term will change the vertical stretch/compression and perhaps reflect the graph across the x axis. Keep in mind that these transformations affect the Domain and Range and asymptotes, too!

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