Use the graph of y = f(x) to graph each function g. g(x) = f(-x)

Verified step by step guidance

1. Step 1: Understand the transformation represented by g(x) = f(-x). This transformation reflects the graph of the original function y = f(x) across the y-axis. For every point (x, y) on the graph of f(x), the corresponding point on g(x) will be (-x, y).
2. Step 2: Identify key points on the graph of y = f(x). These key points might include the x-intercepts, y-intercepts, and any other notable points such as vertices or turning points.
3. Step 3: Apply the reflection transformation to each key point. For each point (x, y) on the graph of f(x), replace x with -x to find the corresponding point on g(x). For example, if a key point is (2, 3), the reflected point will be (-2, 3).
4. Step 4: Plot the reflected points on the graph. Ensure that you maintain the same y-coordinate for each point while flipping the x-coordinate to its opposite sign.
5. Step 5: Connect the reflected points smoothly to form the graph of g(x). Ensure that the overall shape of the graph matches the reflection of the original graph across the y-axis.

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 understanding how to manipulate the coordinates of points based on transformations such as reflections, translations, and stretches. Mastery of these techniques allows for effective visualization of how changes in the function's equation affect its graph.

Coordinate System

The coordinate system is a two-dimensional plane defined by an x-axis (horizontal) and a y-axis (vertical). Each point on this plane is represented by an ordered pair (x, y). Familiarity with the coordinate system is essential for interpreting and graphing functions, as it provides the framework for understanding the position and behavior of graphs.