Question

If f(x) = [x], and g(x) = |x + 2|-3, how is the graph of f(x) translated to form the graph of g(x)?

Answer 1

The graph of f(x) is translated 2 units to the left and 3 units downward to form the graph of g(x).

Step-by-step explanation:

The graph of the function f(x) = [x] can be translated to form the graph of g(x) = |x + 2| - 3 through a series of transformations. First, adding 2 inside the absolute value function in g(x) translates the graph of f(x) 2 units to the left, which is a horizontal translation. This transformation relates to f(x - 2). Then, subtracting 3 from |x + 2| in g(x) translates the graph downward by 3 units, which is a vertical translation.

To summarize the translation:

• Horizontally 2 units to the left.
• Vertically 3 units downward.

This transformation results in the function g(x) from the original function f(x).