Answer
$y$-intercepts: (0, 1), (0, -1)
$x$-intercepts: (1, 0)
Work Step by Step
Set $x=0$ to find $y$-intercept(s):
$y=(0-1)\sqrt (0^2 +1)$
$y=-1(\pm\sqrt (1))$
$y=-1(\pm1)$
$y=\pm1$
Thus, the $y$-intercepts are (0, 1) and (0 -1).
Set $y=0$ to find $x$-intercept(s):
$0=(x-1)\sqrt(x^2+1)$
$x-1=0$ or $\sqrt(x^2+1)=0$
$x=1$ or $x^2+1=0$
$x=1$ or $x^2=-1$
$x=1$ or $x=\sqrt(-1)$
$\sqrt(-1)$ is a non-real result. Thus, the only $x$-intercept is (1, 0).
