# Sketch a graph of the function. Use transformations of functions whenever possible. f(x)=2x^{2} - 1

Question
Transformations of functions
Sketch a graph of the function. Use transformations of functions whenever possible. $$\displaystyle{f{{\left({x}\right)}}}={2}{x}^{{{2}}}\ -\ {1}$$

2021-01-23
First graph function $$\displaystyle{y}={x}^{{{2}}}$$ Then, to obtain graph of function $$\displaystyle{f{{\left({x}\right)}}}={2}{x}^{{{2}}}\ -\ {1},$$ do following transformations: -stretch vertically by a factor of 2 - shift 1 unit downward On graph: Red - $$\displaystyle{y}={x}^{{{2}}}$$ Blue - $$\displaystyle{f{{\left({x}\right)}}}={2}{x}^{{{2}}}\ -\ {1}$$

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