Identify the function in the form (y = alog_b(x-h) + k)
Find the vertical asymptote by setting the log argument equal to 0
Determine the domain from where the log argument is positive
Plot the vertical asymptote as a dashed line
Find the x-intercept by setting (y = 0) and solving for (x)
Find the y-intercept only if (x = 0) is in the domain
Choose several x-values in the domain
Compute the corresponding y-values
Plot the points on the coordinate plane
Use the base (b) to note the general growth pattern
Apply vertical stretch or compression using (|a|)
Reflect across the x-axis if (a < 0)
Shift the graph left or right using (h)
Shift the graph up or down using (k)
Draw a smooth curve through the points approaching the asymptote
Check that the graph stays on the correct side of the asymptote
Verify the graph matches the expected shape of a logarithmic curve