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 united to the left. shift 4 units down

f (x + 5) = |x + 5|, represents the requested change of 5 units to the left,

f (x) - 4 = |x| - 4, represents the requested change of 4 units down.

Step-by-step explanation:

The following rules will permit you to predict the equation of a new function after applying changes, especifically translations, that shift the graph of the parent function in the vertical direction (upward or downward) and in the horizontal direction (left or right).

Horizontal shifts:

Let the parent function be f (x) and k a positive parameter, then f (x + k) represents a horizontal shift of k units to the left, and f (x - k) represents a horizontal shift k units to the right.

Vertical shifts:

Let, again, the parent function be f (x) and, now, h a positive parameter, then f (x) + h represents a vertical shift of h units to upward, and f (x - h) represents a vertical shift of h units downward.

Combining the two previous rules, you get that f (x + k) + h, represents a vertical shift h units upward if h is positive (h units downward if h is negative), and a horizontal shift k units to the left if k is positive (k units to the right if k negative)

Hence, since the parent function is f (x) = |x|

f (x + 5) = |x + 5|, represents the requested change of 5 units to the left,

f (x) - 4 = |x| - 4, represents the requested change of 4 units down.

Furthermore:

f (x + 5) - 4 = |x + 5| - 4, represents a combined shift 5 units to the left and 4 units down.