Sketch a graph. Be sure to include asymptotes and significant points as needed. List the domain and range for each.  Equation: f(x) = ln(|1/2x|)+3  please provide detail explanation.

Expert Answers

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1.Determine for what x values the function is undefined.

Since 1/2x is undefined when x=0, there is an asymptote at x=0

2.Determine the x intercepts by equating to 0




The first solution is:



The second solution is:



The function is symmetric with respect to the x=0 axis.

Evaluate f(x) for a value of x between 0 and 10, say x=5.


Evaluate f(x) for a very high value, say x=`10^10`


The domain is x<0 and x>0

The range is (`-oo,oo)`

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