# 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 - $$\displaystyle{f{{\left({x}\right)}}}={2}{x}^{{{2}}}\ -\ {1}$$ ### Relevant Questions Sketch a graph of the function. Use transformations of functions whenever possible. $$\displaystyle{f{{\left({x}\right)}}}={1}-\sqrt{{{x}}}+{2}$$ Sketch a graph of the function. Use transformations of functions whenever possible. $$\displaystyle{f{{\left({x}\right)}}}={3}{x}^{{{2}}}$$ Sketch a graph of the function. Use transformations of functions whenever possible. $$\displaystyle{f{{\left({x}\right)}}}=-{\left({x}-{1}\right)}^{{{4}}}$$ Sketch a graph of the function. Use transformations of functions whenever possible. $$\displaystyle{f{{\left({x}\right)}}}=\ {\frac{{{1}}}{{{\left({x}\ -\ {1}\right)}^{{{3}}}}}}$$ Sketch a graph of the function. Use transformations of functions whenever possible. $$\displaystyle{f{{\left({x}\right)}}}={\left|{x}\ +\ {1}\right|}$$ Sketch a graph of the function. Use transformations of functions when ever possible.
$$\displaystyle{f{{\left({x}\right)}}}={2}{x}^{{{2}}}-{1}$$ Sketch a graph of the function. Use transformations of functions when ever possible. $$\displaystyle{f{{\left({x}\right)}}}=\sqrt{{{3}}}{\left\lbrace-{x}\right\rbrace}$$ Sketch a graph of the function. Use transformations of functions when ever possible. $$\displaystyle{f{{\left({x}\right)}}}=\ -{\frac{{{1}}}{{{x}^{{{2}}}}}}$$ Sketch a graph of the function. Use transformations of functions when ever possible. $$\displaystyle{f{{\left({x}\right)}}}=\ {\frac{{{1}}}{{{3}}}}{\left({x}\ -\ {5}\right)},\ {2}\ \leq\ {x}\ \leq\ {8}$$ Sketch a graph of the function. Use transformations of functions when ever possible. $$\displaystyle{f{{\left({x}\right)}}}={1}\ -\ \sqrt{{{x}\ +\ {2}}}$$