Identify the logarithm’s base, domain, and vertical asymptote
Rewrite the function in the form (y = alog_b(x-h)+k) if possible
Find the vertical asymptote at (x = h)
Determine the domain: (x-h>0)
Plot the parent function (y=log_b(x)) if needed
Use key parent points such as ((1,0)), ((b,1)), and ((1/b,-1))
Apply horizontal shifts by changing (h)
Apply vertical shifts by changing (k)
Apply vertical stretches or compressions by changing (a)
Reflect across the x-axis if (a<0)
Plot transformed key points
Draw the curve approaching the vertical asymptote
Make sure the graph increases for (b>1)
Make sure the graph decreases for (0 Check that the graph never crosses the vertical asymptote Verify that the graph passes through the transformed point where the log input equals 1 Label the asymptote and key points if required