Question

AI G. Brah is studying the function f(x) shown in the graph. He claims that he can transform the function to include the ordered pair (-3,-1).

a) f(x-1)+2
b) f(x+1)+2
c) f(x-1)-2
d) f(x+1)-2

Answer 1

To include the ordered pair (-3,-1) in the function, the correct transformation would be f(x-1)-2.

Step-by-step explanation:

To transform the function to include the ordered pair (-3,-1), we need to make a horizontal translation of the function. The expression f(x-1) represents a horizontal translation to the right by 1 unit, so it does not include the point (-3,-1). The expression f(x+1) represents a horizontal translation to the left by 1 unit, which also does not include the point (-3,-1).

Option c) f(x-1)-2 represents a horizontal translation to the right by 1 unit and a vertical translation downward by 2 units. This transformation would include the point (-3,-1), since the x-coordinate of the point would shift to -4, and the y-coordinate would shift to -3.

Therefore, the correct option is c) f(x-1)-2.