To determine which translation the function rule [tex]\(T_{-4,6}(x, y)\)[/tex] describes, let's break down what each component of the rule [tex]\(T_{-4,6}\)[/tex] implies.
1. The notation [tex]\(T_{-4,6}\)[/tex] represents a translation transformation in the coordinate plane.
2. Specifically, the rule [tex]\(T_{-4,6}\)[/tex] tells us how to alter the coordinates [tex]\((x, y)\)[/tex].
The components of the function rule are:
- The first number, [tex]\(-4\)[/tex], means we translate the given figure 4 units to the left (negative x-direction).
- The second number, [tex]\(6\)[/tex], means we translate the given figure 6 units up (positive y-direction).
Now let’s analyze each option one by one:
1. A parallelogram on a coordinate plane that is translated 4 units down and 6 units to the right:
- This would correspond to [tex]\(T_{4,-6}(x, y)\)[/tex], not [tex]\(T_{-4,6}(x, y)\)[/tex]. Hence, this is incorrect.
2. A trapezoid on a coordinate plane that is translated 4 units to the left and 6 units up:
- This matches the transformation [tex]\(T_{-4,6}(x, y)\)[/tex] perfectly. Thus, this option is correct.
3. A rhombus on a coordinate plane that is translated 4 units down and 6 units to the left:
- This would correspond to [tex]\(T_{-4,-6}(x, y)\)[/tex], not [tex]\(T_{-4,6}(x, y)\)[/tex]. Hence, this is incorrect.
4. A rectangle on a coordinate plane that is translated 4 units to the right and 6 units up:
- This would correspond to [tex]\(T_{4,6}(x, y)\)[/tex], not [tex]\(T_{-4,6}(x, y)\)[/tex]. Hence, this is incorrect.
Therefore, the correct translation described by the function rule [tex]\(T_{-4,6}(x, y)\)[/tex] is the second option:
- "A trapezoid on a coordinate plane that is translated 4 units to the left and 6 units up."
