# How would you graph #y= -lnx# ?

##### 1 Answer

Jul 28, 2017

Take the graph of

#### Explanation:

Do you know what the graph of

graph{y=e^x [-10, 10, -5, 5]}

- It is monotonically increasing.
- It is always greater than
#0# , so lies completely above the#x# axis. - It is rapidly asymptotic to the
#x# axis for negative values of#x# . - It intersects the
#y# axis at#(0, 1)# . - It grows very rapidly for positive values of
#x# .

Next note that

So the graph of

graph{y=ln x [-10, 10, -5, 5]}

Note that:

- It is monotonically increasing.
- It is only defined for
#x > 0# , so the graph lies entirely to the right of the#y# axis. - It has a vertical asymptote at
#x=0# . - It intersects the
#x# axis at#(1, 0)# . - It grows very slowly for positive values of
#x# .

Finally, to get the graph of

graph{y=-ln x [-10, 10, -5, 5]}

Note that:

- It is monotonically decreasing.
- It is only defined for
#x > 0# , so the graph lies entirely to the right of the#y# axis. - It has a vertical asymptote at
#x=0# . - It intersects the
#x# axis at#(1, 0)# . - It grows more negative very slowly for positive values of
#x# .