Question

What kind of transformation converts the graph of f(x)=|x–6|–6 into the graph of g(x)=|x|–6?

Answer 1

`\mathrm{Domain\:of\:}\:\left|x-6\right|-6\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}`

`\mathrm{Range\:of\:}\left|x-6\right|-6:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\ge \:-6\:\\ \:\mathrm{Interval\:Notation:}&\:[-6,\:\infty \:)\end{bmatrix}`

`\mathrm{Axis\:interception\:points\:of}\:\left|x-6\right|-6:\quad \mathrm{X\:Intercepts}:\:\left(0,\:0\right),\:\left(12,\:0\right),\:\mathrm{Y\:Intercepts}:\:\left(0,\:0\right)`

`\mathrm{Asymptotes\:of}\:\left|x-6\right|-6:\quad \mathrm{None}`

`\mathrm{Extreme\:Points\:of}\:\left|x-6\right|-6:\quad \mathrm{Minimum}\left(6,\:-6\right)`