In Exercises 39–50, graph the given functions, f and g, in the same rectangular coordinate system. Select integers for x, starting with -2 and ending with 2. Once you have obtained your graphs, describe how the graph of g is related to the graph of f. f(x) = -2x, g(x) = -2x-1

Key Concepts

Graphing Linear Functions

Graphing linear functions involves plotting points that satisfy the function's equation on a coordinate plane. Each function can be represented as a straight line, where the slope indicates the steepness and direction of the line, and the y-intercept shows where the line crosses the y-axis. Understanding how to calculate and plot these points is essential for visualizing the relationship between the functions.

Transformation of Functions

Transformation of functions refers to the changes made to the graph of a function based on modifications to its equation. Common transformations include vertical shifts, horizontal shifts, reflections, and stretches or compressions. In this case, the function g(x) = -2x - 1 represents a vertical shift of the function f(x) = -2x downward by 1 unit, which is crucial for understanding their relationship.

Identifying Relationships Between Graphs

Identifying relationships between graphs involves analyzing how one function relates to another in terms of shifts, stretches, or reflections. By comparing the graphs of f and g, one can determine how the transformation affects their positions and shapes. This understanding helps in describing the relationship between the two functions, such as whether one is a translation or a reflection of the other.