Consider the vertically shifted modulus function defined on

MATHEMATICS · Subjective · GCSE · Mathematics · Algebra · Algebra

Problem

Consider the vertically shifted modulus function

g_{k}(x)=|x|+k

defined on

\mathbb R

. (i) Explain how the constant

k\in\mathbb R

affects the minimum value of

g_{k}(x)

. (ii) Hence describe the range of

g_{k}(x)

for the cases: (a)

k>0

, (b)

k=0

, (c)

k<0

. (iii) For

k=-3

, justify whether

g_{k}(x)

is onto

\mathbb R

when viewed as a function from

\mathbb R

\mathbb R