Answer
$(a)$ See the image below
$(b)$
$x$-intercept doesn't exist
$y$-intercepts - $B(0,-2)$
$(c)$ Solving the equation gives us the following:
$x$-intercept never happens
For $y$ intercept:
$x=0$ ; $y=-2$
Work Step by Step
$(a)$ We simply input the equation and get the graph. See the image above.
$(b)$ As we clearly see from the graph, we have no $x$-intercept (The graph approaches $x$-axis but never cross it)
$y$-intercepts - $B(0,-2)$
$(c)$ $y=-\frac{2}{x^2+1}$
For $x$-intercept, we need to find $x$ values where $y=0$
$-\frac{2}{x^2+1}=0$
It will never get $0$ as denominator cannot be $0$. $x$-intercept doesn't exist.
For $y$-intercept, we need to find $y$ values where $x=0$
$y=-\frac{2}{0^2+1}=-\frac{2}{1}=-2$