Question

If you apply the changes below to the absolute value parent function, f(x) = |x|, what is the equation of the new function?Shift 5 units to the left.Shift 4 units down.

Answer 1

Hi! Sorry if this is wrong, but I believe it would be f(x)= |x+5|-4. This is because it shifts to the left, so it is adding 5 to the x in the absolute value bars. And it shifting 4 units down would be negative. Hope this helps!

Answer 2

f(x) = |x+5|; f(x) = |x|-4

Explanation:

A horizontal shift (left or right) will be shown in the function within the operation applied to x.

Since the operation applied to x is absolute value, this means this shift will be shown within the absolute value bars.

A horizontal shift left means the value is added to x before the operator; this means we have x+5 within the bars, or

f(x) = |x+5|

A vertical shift (up or down) will be shown in the function outside of the operation applied to x.

For this function, this means the vertical shift will be outside of the bars; since it is a shift down, we subtract:

f(x) = |x|-4