Write a function rule using function notation that will translate a geometric figure 5 units down and 8 units right.
A. [tex]f(x, y)=(x-5, y+8)[/tex]
B. [tex]f(x, y)=(x-8, y-5)[/tex]
C. [tex]f(x, y)=(x+8, y-5)[/tex]
D. [tex]f(x, y)=(x-5, y-8)[/tex]
Answer (1)
Translates a geometric figure 8 units to the right by adding 8 to the x-coordinate.
Translates the figure 5 units down by subtracting 5 from the y-coordinate.
Combines these translations into a single function rule.
Expresses the translation as: f ( x , y ) = ( x + 8 , y − 5 )
Explanation
Analyze the translation We need to find a function rule that translates a geometric figure 5 units down and 8 units to the right. Let's analyze how each coordinate changes.
Horizontal translation When we translate a point 8 units to the right, we add 8 to its x-coordinate. So, x becomes x + 8 .
Vertical translation When we translate a point 5 units down, we subtract 5 from its y-coordinate. So, y becomes y − 5 .
Function rule Therefore, the function rule that represents this translation is f ( x , y ) = ( x + 8 , y − 5 ) .
Examples
Imagine you're designing a video game. You want to move a character 8 steps to the right and 5 steps down on the screen. This function helps you calculate the new position of the character based on its original position. It's a simple way to update the coordinates of objects in a game or any graphical application.
