In Exercises 1-16, 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 various operations, such as shifting, stretching, or compressing. In this case, the function g(x) = f(x/2) represents a horizontal stretch of the original function f(x) by a factor of 2, meaning that every x-coordinate in the graph of f(x) is doubled in g(x).

Horizontal Stretch

A horizontal stretch occurs when the x-values of a function are multiplied by a factor less than 1. For g(x) = f(x/2), the x-values are effectively halved, which stretches the graph horizontally. This transformation results in the graph of g(x) appearing wider compared to f(x), as points that were originally close together on f(x) will be spaced further apart on g(x).

Graph Interpretation

Graph interpretation involves analyzing the visual representation of a function to understand its behavior and characteristics. In this exercise, students must interpret the graph of f(x) to determine how the points and overall shape will change when applying the transformation to create g(x). Understanding the original graph is crucial for accurately sketching the transformed graph.