Given the following function find the domain, determine vertical asymptote submit graph y=log(x-1) show all your work.Please help

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nathanshields | High School Teacher | (Level 1) Associate Educator

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Think about the graph of y = log x.

This has a vertical asymptote at x = 0 because log 0 is undefined (und).  Why? What exponent could you put onto 10 to make 0?  `10^x=0` ? Similarly, log x is undefined for negative numbers.

y=log(x)

Now, compare log x to log (x-1).  Maybe a little table will help:

x              0         1          2         3

log x        und      0          ~0.3  ~0.5

log x-1     und    und        0      ~0.3

So it appears that all values got shifted to the right by one unit...

In fact, the graph of log(x-1) looks just like the graph of log(x) except shifted right one unit.

So if the vertical asymptote in y = log x occurs at x=0, just shift it over one unit to the right for y = log (x-1).

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