The transformation of a function $\displaystyle {f{{\left({x}\right)}}}$ into a function $\displaystyle {g{{\left({x}\right)}}}$ is given by $\displaystyle {g{{\left({x}\right)}}}={A}{f{{\left({B}{x}+{H}\right)}}}+{K}$.

where the constants

• $\displaystyle {A}$ vertically scales the function. (negative A reflects the function about the x-axis.)
• $\displaystyle {B}$ horizontally scales the function. (negative B reflects the function about the y-axis.)
• $\displaystyle {H}$ horizontally shifts the function.
• $\displaystyle {K}$ vertically shifts the function.

Transform $\displaystyle {f{{\left({x}\right)}}}$ into $\displaystyle {g{{\left({x}\right)}}}$ where the transformation is $\displaystyle {g{{\left({x}\right)}}}=-{f{{\left({x}\right)}}}$

The function $\displaystyle {f{{\left({x}\right)}}}$ is shown below in red. Graph the transformed function $\displaystyle {g{{\left({x}\right)}}}$ by first placing a dot at each end point of the new transformed function and then click on the "line segment" button and connect the two blue dots. (Hint: Use pattern-matching to determine the values of the constants A, B, H, and K.)