Question 407042
First, please put parentheses around the arguments of logarithms. What you posted looks like
y = ln(x) + 4
It is only because you mentioned a vertical asymptote of -4 that I know that the equation is really:
y = ln(x + 4)
These two equations are different and have different graphs. Tutors are more likely to help if the problem is clear.<br>
Since the base of ln is "e", it is difficult to find most ln's without a calculator. So all you have to do is:<ol><li>Pick a value for x, (Note: Since arguments to logarithms must be positive, you must pick a number greater thatn -4!)</li><li>Add 4 to the value of x</li><li>Use your calculator to find the ln of the result of step #2. This will be the value for y.</li><li>Graph this point.</li><li>Repeat all of the above until you can see how the graph goes.</li><li>Draw a smooth curve through the points you've graphes.</li></ol>
If you know what the graph of
y = ln(x)
looks like and if you understand about transformations of graphs, then you could graph
y = ln(x + 4)
very quickly because its graph is exactly the same as the graph of
y = ln(x)
except that it is moved to the left 4 units.