`y=log_2(x-3)` Graph the function. State the domain and range.

We are asked to graph the function `y=log_2(x-3) ` :

The graph is a translation of the graph of `y=log_2x ` 3 units right. Some points on the graph: (25/8,-3),(13/4,-2),(7/2,-1),(4,0),(5,1),(7,2),(11,3)

The domain is x>3; the range is all real numbers. There is a vertical asymptote at x=3, and the x-intercept is x=4. The graph is increasing on its domain, and with calculus it is concave down on its domain.

The graph:

Comments

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