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

Verified step by step guidance

1. Identify the original function f(x) from the graph, which is a horizontal line segment from (1, -3) to (4, -3).
2. Understand that g(x) = f(-x) represents a reflection of f(x) across the y-axis.
3. Reflect each point of f(x) across the y-axis: the point (1, -3) becomes (-1, -3) and the point (4, -3) becomes (-4, -3).
4. Draw the new line segment for g(x) from (-4, -3) to (-1, -3) on the graph.
5. Verify that the new graph of g(x) is a horizontal line segment at y = -3, spanning from x = -4 to x = -1.

Key Concepts

Function Transformation

Function transformation refers to the changes made to the graph of a function based on modifications to its equation. In this case, g(x) = f(-x) represents a horizontal reflection of the function f(x) across the y-axis. Understanding how transformations affect the graph is crucial for accurately sketching 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. For the function g(x) = f(-x), one must identify the corresponding points from f(x) and reflect them across the y-axis to create the graph of g. This skill is essential for interpreting and analyzing functions.

Horizontal Reflection

A horizontal reflection occurs when a graph is flipped over the y-axis. This transformation changes the sign of the x-coordinates of all points on the graph. For example, if a point (a, b) exists on the graph of f(x), then the point (-a, b) will be on the graph of g(x) = f(-x). Recognizing this concept is vital for accurately graphing the transformed function.