Answer:
a) -|x+4|
b) |x-1| -6
Step-by-step explanation:
First, we can compare the functions to f(x)
For (a), the graph seems to be
- flipped upside down
- moved to the left by 4 units (we can tell this because the x intercept is at -4 instead of 0)
First, -f(x) turns a function upside down. Therefore, we have -f(x) = -|x| (this is our new f(x) for (a)). Then, f(x+b) shifts a function b units to the left, so we have f(x+4) = -|x+4|. Note that the 4 is inside the absolute values as it is f(x+b) and not f(x) + b. For f(x+b), we substitute x+b for x. For f(x)+b, we add a b at the end.
For (b), the graph seems to be
- moved to the right by 1 unit (the turning point in the slope is at x=1)
- moved down 6 units (the turning point in the slope is at y=-6)
First, f(x-b) shifts the function b units to the right, so we have f(x-1) = |x-1|
Then, f(x) - b shifts the function b units down, so we have f(x) - 6 = |x-1|-6
