In Exercises 17-32, use the graph of y = f(x) to graph each function g. g(x) = f(-x)

Verified step by step guidance

1. Identify the transformation: The function g(x) = f(-x) represents a reflection of the graph of y = f(x) across the y-axis.
2. Understand the effect of the transformation: For each point (a, b) on the graph of y = f(x), the corresponding point on the graph of g(x) = f(-x) will be (-a, b).
3. Apply the transformation to key points: Take key points from the graph of y = f(x) and reflect them across the y-axis to find their new positions on the graph of g(x).
4. Sketch the new graph: Using the transformed points, sketch the graph of g(x) = f(-x), ensuring that the shape and features of the original graph are preserved, but mirrored across the y-axis.
5. Verify the transformation: Check that the new graph is a mirror image of the original graph with respect to the y-axis, ensuring accuracy in the reflection process.

Key Concepts

Function Reflection

The function g(x) = f(-x) represents a reflection of the function f(x) across the y-axis. This means that for every point (a, b) on the graph of f, there will be a corresponding point (-a, b) on the graph of g. Understanding this concept is crucial for accurately transforming the graph of f into g.

Graphing Techniques

Graphing techniques involve methods for accurately plotting functions on a coordinate plane. This includes identifying key points, understanding the shape of the graph, and applying transformations such as shifts, stretches, and reflections. Mastery of these techniques is essential for visualizing how g(x) relates to f(x).

Coordinate System

A coordinate system provides a framework for locating points in a plane using ordered pairs (x, y). In the context of graphing functions, it is important to understand how changes in the x-values affect the corresponding y-values. This understanding is fundamental when applying transformations like the reflection in g(x) = f(-x).