Question

A)i.Write the the absolute value function y=|2x+5|+3|x-1| as a piece-wise function.

ii)What is the range?​

Answer 1

Explanation:

for |2x+5|=

`\left \{ {{2x+5}~~~~if~~~~2x+5 > 0 ~~or ~~~~x>(-5)/(2)~~(case 1) \\ \atop {-2x-5}} ~~~~~if~~~2x+5 <0 ~~~~or~~~x<(-5)/(2)~~(case 2)`

for |x-1| =
`\left \{ {{x-1 } ~~~~if~~~x-1>0 ~~~or~~~x>1 ~~(case 3)\atop {1-x}} ~~~~if ~~~~x-1<0 ~~~~or~~~x<1 \right. (case 4)`