Answer:
y = |x+3| - 4
Step-by-step explanation:
Topic: Transforming Functions
You have to be familiar on how functions change according to certain factors, let's suppose we have a function y = f(x), if i add/substract to the function a constant a, as y = f(x) ± a it will move up in y axis (if it's +) or down in y axis (if it's -), a units.
If the function is applied to the argument like y = f(x ± a) it will move to the right the function a units (if it's - ) and to the left a units (if its +). so for this function we have.
you know that the function that does this V shaped figure is |x|
so you have that y = |x| it would be centered on (0,0) as you can see in the first image.
but you know it is moved 3 units to the left on the x axis. so we have to add + 3 to the argument in this case and you get the second image plotting y = |x+3|
and for last you know that the function is moved - 4 units in y axis. so you have to substract 4 from the function having the 3 image and the same of the problem, so the function you are looking for is y = |x+3| - 4
and there's no correct option in the options available.
but the correct option is y = | x + 3 | - 4 check it on geogebra
also i encourage you to find out other types of transforming functions.
