A function is defined on by .

MATHEMATICS · Multi-part · AoPS · Mathematics · Special Functions · Special Functions

Problem

A function

h

is defined on

\mathbb{R}

h(x)=|x+1|-3\,\operatorname{sgn}(x-2)

. (i) Rewrite

h(x)

in explicit piecewise form, stating the interval for every expression obtained. (ii) Solve the equation

h(x)=0

. (iii) Determine the domain, range,

x

‑intercept(s) and

y

‑intercept of

h

. (iv) Sketch the graph of

y=h(x)

on the interval

-5 \le x \le 5

, marking all intercepts and points of discontinuity, if any.