In Exercises 33-44, use the graph of y = f(x) to graph each function g. g(x) = f(x+2)

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 function g(x) = f(x + 2) represents a horizontal shift of the graph of f(x) to the left by 2 units. Understanding how transformations affect the position and shape of a graph is crucial for accurately graphing the new function.

Horizontal Shifts

Horizontal shifts occur when a function is modified by adding or subtracting a value from the input variable. For g(x) = f(x + 2), the '+2' indicates that every point on the graph of f(x) moves 2 units to the left. This concept is essential for predicting how the original graph will change and for accurately plotting the new function.

Graphing Functions

Graphing functions involves plotting points on a coordinate plane to visually represent the relationship between the input (x) and output (y) values of a function. To graph g(x) = f(x + 2), one must first understand the original graph of f(x) and then apply the horizontal shift. This skill is fundamental in algebra as it helps in visualizing and interpreting mathematical relationships.