When Suwanda shifts a triangle (or any shape) 2 units to the right on a coordinate grid, the function representing this transformation will adjust the input \( x \) value of the function by subtracting 2.
The general transformation for a horizontal shift to the right by \( h \) units is given by:
\[ f(x) \rightarrow f(x - h) \]
In this case, \( h = 2 \), so the function will be:
\[ f(x) \rightarrow f(x - 2) \]
This means that each point \( (x, y) \) on the original triangle will be moved to \( (x + 2, y) \).
The transformations given in the options provided don't explicitly handle a shift in the form \( f(x - 2) \). However, they present linear equations which might imply transformations of basic functions, particularly linear ones.
Among the options provided, none are explicitly the transformation function representing a shift. However, if you were to analyze the slope and y-intercept based on the shift, you might say:
- \( f(x) = -x + 2 \) remains a linear function that does not represent a right shift.
- \( f(x) = 2 - x \) is also a linear function not linked to the rightward shift directly.
- \( f(x) = x + 2 \) is a linear function that effectively represents a vertical shift upwards rather than shifting the triangle horizontally.
- \( f(x) = -2 - x \) also does not represent a rightward shift.
Thus, none of the options directly represent the idea of shifting a triangle 2 units to the right, as there is no perfect match to the transformation being described. If you need to represent the shift mathematically, you'd typically start with a basic function (like \( f(x) = x \)) and adjust it accordingly.
If there were more context or if there were modifications to these functions to better reflect a shift, that could clarify further. However, in the current offerings, none suffice for a horizontal shift right by 2 units specifically.
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