In Exercises 1-16, use the graph of y = f(x) to graph each function g.
g(x) = f(x-1) - 2

Key Concepts

Function Transformation

Function transformations involve changing the position or shape of a graph through various operations. In this case, g(x) = f(x-1) - 2 represents a horizontal shift to the right by 1 unit and a vertical shift downward by 2 units. Understanding these transformations is crucial for accurately graphing the new function based on the original function f(x).

Horizontal Shift

A horizontal shift occurs when the input of a function is altered, affecting the graph's position along the x-axis. For g(x) = f(x-1), the graph of f(x) is shifted to the right by 1 unit. This means that every point on the graph of f(x) will move right, which is essential for determining the new coordinates of g(x).

Vertical Shift

A vertical shift changes the position of a graph along the y-axis. In the function g(x) = f(x-1) - 2, the '-2' indicates that the entire graph of f(x) is moved down by 2 units. This transformation affects the y-coordinates of all points on the graph, which is necessary for accurately plotting g(x) after applying the horizontal shift.