Question

the graph below shows a transformation of a linear function where the line ab is the pre-image and the line ab is the image. which of the following correctly describes the transformation?

• translation up 3 or ((x, y + 3))
• (90^circ) rotation about point (a)
• reflection over (y)-axis
• translation down 3 or ((x, y - 3))
• translation right 3 or ((x + 3, y))
• translation left 3 or ((x - 3, y))

Explanation:

To determine the transformation, we analyze the coordinates of points \( A \), \( B \) and their images \( A' \), \( B' \). Let's assume the coordinates: from the graph, \( A \) seems to be at \((-1, 9)\) and \( A' \) at \((-1, 6)\); \( B \) at \((0, 5)\) and \( B' \) at \((0, 2)\). The \( x \)-coordinates remain the same, and the \( y \)-coordinates decrease by 3 (e.g., \( 9 - 3 = 6 \), \( 5 - 3 = 2 \)). This indicates a vertical translation down 3 units, represented as \((x, y - 3)\). Other options: rotation would change the slope, reflection over \( y \)-axis would flip \( x \)-coordinates, and horizontal translations would change \( x \)-coordinates, which is not the case here.

Answer:

Translation down 3 or \((x, y - 3)\)