The graph of a function ƒ is shown in the figure. Sketch the graph of each function defined as follows.
(b) y = ƒ(x-2)

Key Concepts

Function Transformation

Function transformations involve changing the position or shape of a graph based on specific rules. In this case, the transformation y = ƒ(x-2) indicates a horizontal shift of the graph of ƒ to the right by 2 units. Understanding how transformations affect the graph is crucial for accurately sketching the new function.

Horizontal Shifts

A horizontal shift occurs when the input variable of a function is altered by adding or subtracting a constant. For y = ƒ(x-2), the '-2' indicates that every point on the graph of ƒ will move 2 units to the right. This concept is essential for predicting the new coordinates of points on the transformed graph.

Graphing Functions

Graphing functions involves plotting points on a coordinate plane based on the function's output for various inputs. To sketch the graph of y = ƒ(x-2), one must take the original points from the graph of ƒ and apply the horizontal shift. This skill is fundamental in visualizing how functions behave and interact with one another.