Question

Simplify : $f\left(x\right)=\left|x+4-3+2-11+100\right|$

Answer 1

$\mathrm{Simplify}\:\left|x+4-3+2-11+100\right|:\quad \left|x+92\right|$

$\left|x+4-3+2-11+100\right|$

$\mathrm{Add/Subtract\:the\:numbers:}\:4-3+2-11+100=92$

$=\left|x+92\right|$

$\mathrm{Domain\:of\:}\:\left|x+92\right|\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}$

$\mathrm{Range\:of\:}\left|x+92\right|:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\ge \:0\:\\ \:\mathrm{Interval\:Notation:}&\:[0,\:\infty \:)\end{bmatrix}$

$\mathrm{Axis\:interception\:points\:of}\:\left|x+92\right|:\quad \mathrm{X\:Intercepts}:\:\left(-92,\:0\right),\:\mathrm{Y\:Intercepts}:\:\left(0,\:92\right)$

Answer 2

| x+4-3-11+100 |=90+x

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