Question

How does changing the h and k values in an absolute value function change the graph from f(x) = |x|? Fully describe the movement for both h and k.

Answer 1

In an absolute value function f(x) = |x - h| + k, the h value causes horizontal translations, and the k value causes vertical translations of the graph.

Step-by-step explanation:

Changing the h and k values in an absolute value function affects the graph's position relative to the standard f(x) = |x|. When we have a function in the form f(x) = |x - h| + k, the value of h will horizontally translate the graph. If h is positive, the graph moves to the right; if h is negative, the graph moves to the left. On the other hand, the value of k vertically translates the graph. A positive k value moves the graph upward, whereas a negative k value moves it downward.