Question

Consider the function f(z) = |z| + 3. What is the translation applied to the parent absolute value function?

A) Three units to the left.
B) Three units up.
C) Three units to the right.
D) Three units down.

Answer 1

The function f(z) = |z| + 3 is the parent absolute value function translated three units up on the coordinate plane, with no horizontal shift.

The translation applied to the parent absolute value function in the function f(z) = |z| + 3 is three units up. This is recognized by the '+3' which indicates a vertical shift in the positive y-direction of the graph of the parent function. No horizontal translation is indicated because the variable z has not been altered inside the absolute value.

Remember, a function f(x) translated vertically upward adds a positive constant outside the function (e.g., f(x) + d), and when the constant is positive, there is no direction change, so it moves upward. Conversely, if it were a minus (e.g., f(x) - d), the graph would move downward.

for the given function the absolute value graph is simply shifted up three units without any horizontal movement.