Mathematics

Problem

A function

h: \mathbb R \to \mathbb R

is defined by

h(x)=|x^{2}-6x+8|

. a. (i) Factorise

x^{2}-6x+8

and identify the intervals on which this quadratic expression is non-negative and negative. b. (ii) Using the result of part (i), rewrite

h(x)

as a piecewise function without the modulus sign. c. (iii) Determine the range of

h

by analysing the two pieces obtained in part (ii).