Question

let g(x) be the transformation of f(x) = |x| right 2 units. identify the rule for g(x) and its graph.

Answer 1

The rule for g(x) is g(x) = |x - 2|. The graph of g(x) is identical to the graph of f(x), but shifted two units to the right.

Step-by-step explanation:

To find the rule for g(x), which represents the transformation of f(x) = |x| right 2 units, we need to shift the graph of f(x) two units to the right. This can be achieved by replacing x in the equation f(x) with (x - 2), resulting in g(x) = |x - 2|. The graph of g(x) will be identical to the graph of f(x), but shifted to the right by two units.

Example: If we take the point (2, 2) on the graph of f(x), after the transformation, it will become (4, 2) on the graph of g(x).

Answer 2

To identify the rule for g(x) when f(x) = |x| is translated right by 2 units, you would use the function g(x) = |x - 2|. The graph of g(x) will look like the graph of |x|, but shifted 2 units to the right.

The question asks about the transformation of the function f(x) = |x| when it is shifted to the right by 2 units. This operation is identified in algebra as a horizontal shift. We can denote the transformed function as g(x).

When a function f(x) is shifted to the right by d units, the new function can be described as f(x - d). In this case, since the shift is 2 units to the right, the new function will be f(x - 2), or since our original function f(x) is |x|, the transformation will be g(x) = |x - 2|.

The graph of this function starts at the point (2, 0) and increases linearly in both the positive and negative directions from that point. To accurately depict this on a graph, label the axes as x and f(x), choose a scale that fits the domain 0≤x≤2, and then plot the function accordingly, considering that the vertex of the graph has been moved from (0, 0) to (2, 0).

The graph is shown below: