Question

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

Answer 1

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 - \(\displaystyle{f{{\left({x}\right)}}}={2}{x}^{{{2}}}\ -\ {1}\)