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

Key Concepts

Function Transformation

Function transformation refers to the process of altering the graph of a function through shifts, stretches, or reflections. In this case, the transformation involves a horizontal shift, which affects the x-coordinates of the function's graph. Understanding how to apply these transformations is crucial for accurately graphing the new function g(x) based on f(x).

Horizontal Shift

A horizontal shift occurs when a function is moved left or right on the Cartesian plane. For the function g(x) = f(x + 1), the graph of f(x) is shifted to the left by 1 unit. This shift changes the x-values of all points on the graph, which is essential to visualize the new function correctly.

Graphing Functions

Graphing functions involves plotting points on a coordinate system to represent the relationship between the input (x) and output (y) values. To graph g(x) = f(x + 1), one must first understand the original graph of f(x) and then apply the horizontal shift to each point. This skill is fundamental in algebra for visualizing and interpreting functions.