how do you graph y=lnx+3

Question

and find the domain and range. y=lx+3 graph??

Answer 1

 

First step.  you can get the picture of ln(x): http://upload.wikimedia.org/wikipedia/co…

Second step, you just have to edge it to the left by three units.

Answer 2

To graph, simply create a table of values for x and y (when x is __,  y is __ ). Although if you know the basic parent function of ln(x), then this one is simply shifted to the left by three units.

For the domain, that means all values of x that satisfy the equation. Therefore, we have to know what values of x are invalid. 

For logarithms, values of x must be positive and greater than zero. So we find the conditions that would violate it (what values of x would cause this to happen?):

x + 3 > 0

x > -3

So only values of x that are > -3 (but not equal to) would satisfy the equation. So the domain in interval notation is

(-3, +inf)

The range are all the corresponding values of y, which begin at neg inf and go to pos inf (though very slowly, e.g.,  y = ln(1x10^100) = 230).

So the range is (-inf., +inf)

Use a graphing utility to see for yourself.