Question

c. then, the robot flips its arms (moves its right arm up and its left arm down).
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)
this type of transformation would be called a reflection.

Explanation:

Step1: Identify transformation type

Flipping right/left arms swaps left/right, matching reflection over the vertical axis (y-axis), which is a reflection transformation.

Step2: Apply reflection to function

A reflection over the y-axis replaces $x$ with $-x$ in the original function $f(x) = x^3$. Substitute $-x$ into the function:
$g(x) = f(-x) = (-x)^3$
Simplify the expression: $(-x)^3 = -x^3$

Answer:

i. Reflection
ii. $g(x) = -x^3$