I REALLY NEED HELPPPPP Identify all of the transformation effects on the graph of the function ƒ(x) = x when ƒ(x) is replaced with −ƒ(x + 4) − 6

A) shifted up 6 units
B) shifted down 6 units
C) shifted left 4 units
D) shifted right 4 units
E) reflected over x-axis


  1. Answers:
    • B) Shifted down 6 units
    • C) Shifted left 4 units
    • E) Reflected over x-axis
    The negative out front of the function tells us that we’re multiplying the y coordinates by -1. This moves any (x,y) point to (x,-y). For example, a point like (1,2) moves to (1,-2). This is an x-axis reflection.
    The jump from x to x+4 means the xy axis has moved 4 units to the right. Any input is now 4 units larger. If we kept the curve fixed in place while the axis moved, this gives the illusion the curve moves 4 units to the left.
    Lastly the -6 at the very end will subtract 6 off whatever the y value is. This visually shifts the graph down 6 units.


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