Graph $f(x,y)=\ln(x)-y$

Question

I'm trying to graph $f(x,y)=\ln(x)-y$, however, I am not sure how as all of my tools are refusing to graph it.

Can you please help me?

Thanks

Answer 1

You cannot draw it on the $Oxy$-plane. You have two input values $x$ and $y$ and so you need one more axis to represent the value of $f$. Below is the graph drawn via GeoGebra:

Answer 2

Note that there is no way to plot this in 2D because you would need an equation of the form $f(x,y) = 0$, and what you have is $f(x,y) = \ln(x) - y$, which can be thought of as $f(x,y) = z$. That means you need a 3D plot to visualize it.

There are several good online options for plotting 3D graphs. Here are two good ones:

1.) Calcplot3D, which produces the following plot. This one is my personal favorite, but you might want to see here for key commands for camera controls.

2.) Geogebra, which produces the plot