Question

A piecewise linear function is graphed below. (see image)

Fill in all of the blanks to give an algebraic description of the function.

y = ___ for x < ___
___ for ___ ≤ x < ___
___for x ≥ ___

Answer 1

y = 2 for x < 0
= x for 0 ≤ x < 3
= 3 for x ≥ 3

Answer 2

Explanation:

Given is a piecewise graph

discontinuous at x=0

For all negative x, we have y = constant = 2

Hence I part is

y =2, for x<0

Next part is from x=0 to x=3

Passes through points (0,0) and (3,3)

Hence equation is y =3x for
`0\leq x\leq 3`

For all values of x >3, we have a horizontal line as y = 3

Consolidated together

`y=x, for x<0\\y=3x, for 0\leq <3\\y=3, for x\geq 3`