To determine which translation is described by the function rule [tex]\( T_{-4,6}(x, y) \)[/tex], let's break down what this function rule means:
1. The notation [tex]\( T_{-4,6}(x, y) \)[/tex] represents a translation transformation. In this context, a translation means shifting every point of a shape the same distance in a specified direction.
2. [tex]\( T_{-4,6} \)[/tex] indicates how much the shape is moved along the x-axis and y-axis. Specifically:
- The value [tex]\(-4\)[/tex] indicates a movement of 4 units in the negative x-direction, which means 4 units to the left.
- The value [tex]\(6\)[/tex] indicates a movement of 6 units in the positive y-direction, which means 6 units up.
Therefore, [tex]\( T_{-4,6}(x, y) \)[/tex] translates any shape on the coordinate plane 4 units to the left and 6 units up.
Given the options:
- A parallelogram on a coordinate plane that is translated 4 units down and 6 units to the right: This is incorrect because the translation implies a different direction (-4,6) contradicting (4,-6).
- A trapezoid on a coordinate plane that is translated 4 units to the left and 6 units up: This description matches our identified translation, which is precisely what [tex]\( T_{-4,6}(x, y) \)[/tex] does.
- A rhombus on a coordinate plane that is translated 4 units down and 6 units to the left: This description implies a translation of (-4, -6), which is not the case here.
- A rectangle on a coordinate plane that is translated 4 units to the right and 6 units up: This description represents a translation of (4, 6), which does not match our translation parameters.
After considering all the options, it is clear that the function rule [tex]\( T_{-4,6}(x, y) \)[/tex] describes the translation of:
A trapezoid on a coordinate plane that is translated 4 units to the left and 6 units up.
