Question

Which of these function(s) have a graph that is a translation of the graph of f(x) = x? Select all that apply.

A. g(x) = 2x
B. h(x) = x + 1
C. j(x) = x − 2
D. k(x) = 1/2x

Answer 1

Functions h(x) = x + 1 and j(x) = x - 2 represent translations of the graph of the function f(x) = x, shifting the graph without changing its shape.

Step-by-step explanation:

The question asks which functions represent a translation of the graph of the linear function f(x) = x. A translation in terms of graphing means shifting the graph horizontally or vertically without changing its shape or orientation.

Starting with the original function f(x) = x, we know that:

• g(x) = 2x is not a translation but a stretch by a factor of 2.
• h(x) = x + 1 represents a translation by 1 unit downward in the y-direction.
• j(x) = x - 2 represents a translation by 2 units upward in the y-direction.
• k(x) = 1/2x is also not a translation but a compression by a factor of 1/2.

Therefore, functions h(x) and j(x) are translated versions of f(x).