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 by a multiplier of A. (Negative A reflects the function about the x-axis.)
• $\displaystyle {B}$ horizontally scales the function by a multiplier of 1/B. (Negative B reflects the function about the y-axis.)
• $\displaystyle {H}$ horizontally shifts the function by H units. (Negative H shifts the function to the right.)
• $\displaystyle {K}$ vertically shifts the function by K units. (Negative K shifts the function down.)

Transform $\displaystyle {f{{\left({x}\right)}}}$ into $\displaystyle {g{{\left({x}\right)}}}$ where the transformation is $\displaystyle {g{{\left({x}\right)}}}={f{{\left({x}-{1}\right)}}}+{3}$

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: Transform the function by applying the constants in this order: H, B, A, K. First place the two blue dots by shifting the function by H units. Then move the two blue dots by using a multiplier of 1/B. Likewise, continue for A and K. Finally connect the final position of the blue dots with the line segment.