# Sketch a graph of the function. Use transformations of functions whenever possible. f(x)= frac{1}{(x - 1)^{3}}

Question
Transformations of functions
Sketch a graph of the function. Use transformations of functions whenever possible. $$\displaystyle{f{{\left({x}\right)}}}=\ {\frac{{{1}}}{{{\left({x}\ -\ {1}\right)}^{{{3}}}}}}$$

2020-11-10
Step 1 First graph function $$\displaystyle{y}=\ {\frac{{{1}}}{{{x}^{{3}}}}}.$$ Then, to obtain graph of function $$\displaystyle{f{{\left({x}\right)}}}=\ {\frac{{{1}}}{{{\left({x}\ -\ {z}\right)}^{{{3}}}}}}$$, do following transfromations: - shift 1 unit to the right. On graph: Red: $$\displaystyle{y}=\ {\frac{{{1}}}{{{x}^{{{3}}}}}}$$ Blue: $$\displaystyle{f{{\left({x}\right)}}}=\ {\frac{{{1}}}{{{\left({x}\ -\ {1}\right)}^{{{3}}}}}}$$ Step 2

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