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Advanced Functions

Given the functions 𝑓(π‘₯) = π‘™π‘œπ‘”_3 (3π‘₯) and 𝑔(π‘₯) = π‘™π‘œπ‘”_3 (π‘₯) + 1
a. Describe the transformations applied to each function.
b. How do the graphs of the two functions compare? Explain your answer by referring to logarithmic
laws and properties.

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  1. log3(3x) = log3(3) + log3(x) = 1 + log3(x)
    f(x) is identical to g(x)

    g(x) is f(x)
    dilated in x by 3
    shifted up 1
    The two transformations cancel each other out

    the graphs of all exponential functions look the same
    dilating and shifting are complementary operations.

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    oobleck

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