Question

If the parent function f(x) = |x| is transformed to g(x) = |x − 3|, what transformation occurs from f(x) to g(x)?

Answer 1

The transformation from f(x) = |x| to g(x) = |x - 3| is a horizontal translation to the right by 3 units.

Step-by-step explanation:

To understand this, recall from algebra that if f(x) is any function, then f(x − d) represents the function f shifted horizontally to the right by a distance d units.

The transformation from the parent function f(x) = |x| to the function g(x) = |x - 3| is a horizontal translation to the right by 3 units.

When we subtract 3 from x in the absolute value function, it shifts the graph 3 units to the right.

For example, if we take the point (0, 0) on the graph of f(x) = |x|, after the transformation, it will be located at (3, 0) on the graph of g(x) = |x - 3|.