To understand the function rule [tex]\( T_{-4,6}(x, y) \)[/tex], we need to analyze what the translation parameters [tex]\((-4, 6)\)[/tex] represent.
1. In the context of translation on a coordinate plane, the [tex]\( x \)[/tex]-coordinate translation parameter affects the horizontal movement:
- A positive value for the [tex]\( x \)[/tex]-coordinate means moving to the right.
- A negative value for the [tex]\( x \)[/tex]-coordinate means moving to the left.
2. The [tex]\( y \)[/tex]-coordinate translation parameter affects the vertical movement:
- A positive value for the [tex]\( y \)[/tex]-coordinate means moving up.
- A negative value for the [tex]\( y \)[/tex]-coordinate means moving down.
Given the translation parameters [tex]\( (-4, 6) \)[/tex]:
- The [tex]\( x \)[/tex]-coordinate is [tex]\(-4\)[/tex], which indicates a shift of 4 units to the left.
- The [tex]\( y \)[/tex]-coordinate is [tex]\( 6 \)[/tex], which indicates a shift of 6 units up.
Thus, [tex]\( T_{-4,6}(x, y) \)[/tex] translates a shape on a coordinate plane 4 units to the left and 6 units up.
Next, let's match this translation to the options provided:
1. a parallelogram on a coordinate plane that is translated 4 units down and 6 units to the right - This option describes a translation of [tex]\((4, -6)\)[/tex], which is not what we have.
2. a trapezoid on a coordinate plane that is translated 4 units to the left and 6 units up - This option accurately describes our translation of [tex]\((-4, 6)\)[/tex].
3. a rhombus on a coordinate plane that is translated 4 units down and 6 units to the left - This option describes a translation of [tex]\((-6, -4)\)[/tex], which is incorrect.
4. a rectangle on a coordinate plane that is translated 4 units to the right and 6 units up - This option describes a translation of [tex]\((4, 6)\)[/tex], which is not correct.
Therefore, the correct answer is:
A trapezoid on a coordinate plane that is translated 4 units to the left and 6 units up.
