Question

If f(x) = |x| and g(x) = x^1 - 4, which translation is applied to Ax) to get g(x)?

Option 1: Horizontal shift to the right by 4 units.
Option 2: Vertical shift up by 4 units.
Option 3: Horizontal shift to the left by 4 units.
Option 4: Vertical shift down by 4 units.

Answer 1

The correct translation from f(x) = |x| to g(x) = x - 4 is a horizontal shift to the left by 4 units, which is Option 3.

Step-by-step explanation:

To determine which translation is applied from f(x) = |x| to g(x) = x - 4, we need to understand how transformations affect the graph. According to algebra, for any function f(x), the form f(x - d) translates the function horizontally to the right by d units, and the form f(x + d) translates it horizontally to the left by d units. Since g(x) is obtained by subtracting 4 from x, we are dealing with a horizontal shift to the left by 4 units. Therefore, the correct answer is Option 3: Horizontal shift to the left by 4 units.