Answer
$y$-intercept: $\dfrac{1}{3}$
$x$-intercepts: $2$ and $-1$
Work Step by Step
$t(x)=\dfrac{x^{2}-x-2}{x-6}$
Substitute $t(x)$ by $y$:
$y=\dfrac{x^{2}-x-2}{x-6}$
To find the $y$-intercept, set $x$ equal to $0$ and solve for $y$:
$y=\dfrac{(0)^{2}-0-2}{0-6}=\dfrac{-2}{-6}=\dfrac{1}{3}$
To find the $x$-intercept, set $y$ equal to $0$ and solve for $x$:
$0=\dfrac{x^{2}-x-2}{x-6}$
$(0)(x-6)=x^{2}-x-2$
$x^{2}-x-2=0$
Solve by factoring:
$(x-2)(x+1)=0$
Set both factors equal to $0$ and solve each individual equation for $x$:
$x-2=0$
$x=2$
$x+1=0$
$x=-1$
$y$-intercept: $\dfrac{1}{3}$
$x$-intercepts: $2$ and $-1$