Question

The equation y = - |x + 5|describes a function that is translated from a parent function. What graph represents this translation?

Answer 1

Graph and its translation

We first graph y = x

We know y = |x|, is just as the previous graph but the negative values of y are positive, then on those part it gets reflected

The graphic of y = -|x| is just like the previous graph but since all the values have opposite signed it gets totally reflected:

We know that if we add a number to x if will be translated to the left and if we subtract a number it will be translated to the right. Then y = -|x+5| has the same graphic as y = -|x| but it is translated to the left 5 places