Answer
(a) According to the graph, the function intercepts the x-axis when $x=-1$
The x-intercept is: $(-1,0)$
(b) Algebraically $y=0$ when $x=-1$
The x-intercept is: $(-1,0)$
Work Step by Step
$y=x+2+\frac{1}{x}$
$0=x+2+\frac{1}{x}~~$ (Multiply both sides by $x$)
$0=x^2+2x+1=x^2+2(1)x+1^2$
$(x+1)^2=0$
$x+1=0$
$x=-1$
