Continuity and differentiability of a function defined parametrically

Question

How do we check continuity and differentiability of a function defined parametrically e.g. $$x=2t-|t-1|$$ and $$y=2t^2+t|t|$$

Answer 1

I prefer to consider it as a vector function $$r(t)=x(t)\vec{i}+y(t)\vec{j}$$ in $\mathbb{R}^2 $.

Answer 2

$t\longmapsto (x_1(t),...,x_n(t))$ is continuous and differntiable $\iff$ $t\longmapsto x_i(t)$ is continuous and differentiable for all $i$.