# Sketch a graph of the function. Use transformations of functions when ever possible. f(x)=sqrt[3]{-x}

Question
Transformations of functions
Sketch a graph of the function. Use transformations of functions when ever possible. $$\displaystyle{f{{\left({x}\right)}}}=\sqrt{{{3}}}{\left\lbrace-{x}\right\rbrace}$$

2021-01-17
Step 1
Shown is the graph of $$\displaystyle{f{{\left({x}\right)}}}=\sqrt{{{3}}}{\left\lbrace-{x}\right\rbrace}$$
x is on the horizontal axis and y is on the vertical axis.
Step 2

### Relevant Questions

For each of the following functions f (x) and g(x), express g(x) in the form a: f (x + b) + c for some values a,b and c, and hence describe a sequence of horizontal and vertical transformations which map f(x) to g(x).
$$\displaystyle{f{{\left({x}\right)}}}={x}^{{2}}+{3},{g{{\left({x}\right)}}}={x}^{{2}}-{6}{x}+{8}$$
Sketch a graph of the function. Use transformations of functions when ever possible. $$\displaystyle{f{{\left({x}\right)}}}={1}\ -\ \sqrt{{{x}\ +\ {2}}}$$
For each of the following functions f (x) and g(x), express g(x) in the form a: f (x + b) + c for some values a,b and c, and hence describe a sequence of horizontal and vertical transformations which map f(x) to g(x).
$$\displaystyle{f{{\left({x}\right)}}}={x}^{{2}}-{2},{g{{\left({x}\right)}}}={2}+{8}{x}-{4}{x}^{{2}}$$
For each of the following functions f (x) and g(x), express g(x) in the form a: f (x + b) + c for some values a,b and c, and hence describe a sequence of horizontal and vertical transformations which map f(x) to g(x).
$$\displaystyle{f{{\left({x}\right)}}}={x}^{{2}},{g{{\left({x}\right)}}}={3}{x}^{{2}}-{24}{x}+{8}$$
For each of the following functions f (x) and g(x), express g(x) in the form a: f (x + b) + c for some values a,b and c, and hence describe a sequence of horizontal and vertical transformations which map f(x) to g(x).
$$\displaystyle{f{{\left({x}\right)}}}={x}^{{2}},{g{{\left({x}\right)}}}={2}{x}^{{2}}+{4}{x}$$
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. $$\displaystyle{f{{\left({x}\right)}}}=\ {\frac{{{1}}}{{{\left({x}\ -\ {1}\right)}^{{{3}}}}}}$$
$$\displaystyle{f{{\left({x}\right)}}}={2}{x}^{{{2}}}-{1}$$
$$\displaystyle{f{{\left({x}\right)}}}={\left|{x}+{1}\right|}$$
Sketch a graph of the function. Use transformations of functions when ever possible. $$\displaystyle{f{{\left({x}\right)}}}=\ -{\frac{{{1}}}{{{x}^{{{2}}}}}}$$