Question

b. assume that after each dance move, the robot always returns to its original position of $f(x) = x^3$. next, the robot moves to the left 2 units.
i. what type of transformation would this be (rotation, reflection, translation, stretch, compression)?
ii. what would the new equation be (based on the original equation of $f(x) = x^3$)?
(2 points)

Explanation:

i. Moving a function left/right without changing its shape, orientation, or size is a horizontal translation, which falls under the translation category of transformations.
ii. For a horizontal shift left by $h$ units, the transformation rule is $f(x) \to f(x+h)$. Here, $h=2$ and the original function is $f(x)=x^3$.

Answer:

i. Translation (specifically horizontal translation)
ii. $f(x)=(x+2)^3$