A function is defined by .

MATHEMATICS · Multi-part · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

A function

h: \mathbb R \to \mathbb R

is defined by

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

. (i) Factorise

x^{2}-6x+8

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

h(x)

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

h

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