# How do you graph f(x)= x ln (x) - x?

Nov 11, 2017

See below.

#### Explanation:

No y axis intercepts since $\ln \left(0\right)$ is undefined.

$x$ axis intercepts where $y = 0$.

$x \ln x - x = 0$

$x \ln x = x \implies \ln x = 1 \iff {e}^{1} = x$

x axis intercept at $\left(e , 0\right)$

as $x \to \infty$ , $\textcolor{w h i t e}{88} x \ln x - x \to \infty$

Graph:

graph{y=x(lnx)-x [-10, 10, -5, 5]}