Answer
(a) According to the graph, it is seems that the function intercepts the x-axis in two points. But, it is not clear enough.
(b) Algebraically $y=0$ when $x=1$ and when $x=2$
The x-intercepts are: $(1,0)$ and $(2,0)$
Work Step by Step
$y=x-3+\frac{2}{x}$
$0=x-3+\frac{2}{x}~~$ (Multiply both sides by $x$)
$0=x^2-3x+2=x^2-x-2x+2$
$x(x-1)-2(x-1)=0$
$(x-2)(x-1)=0$
$x-2=0$
$x=2$
$x-1=0$
$x=1$
