Use the graphs of f and g to solve Exercises 83–90.

Graph f+g.

Verified step by step guidance

1. Observe the graph of f(x) (blue line) and g(x) (orange line). The goal is to graph the sum of the two functions, f(x) + g(x), by adding their y-values at each x-coordinate.
2. Identify the x-coordinates where both functions are defined. These are the points where the graphs overlap horizontally. For this graph, the x-values range from -6 to 8.
3. For each x-coordinate, add the corresponding y-values of f(x) and g(x). For example, at x = -6, f(-6) = 6 and g(-6) = -6, so f(-6) + g(-6) = 6 + (-6) = 0.
4. Repeat the addition process for all x-coordinates where both functions are defined. For instance, at x = -4, f(-4) = 6 and g(-4) = -4, so f(-4) + g(-4) = 6 + (-4) = 2.
5. Plot the resulting points (x, f(x) + g(x)) on the graph and connect them to form the graph of f + g. Ensure the graph reflects the combined behavior of the two functions.

Key Concepts

Function Addition

Function addition involves combining two functions, f(x) and g(x), to create a new function, (f + g)(x) = f(x) + g(x). This means that for each input x, you calculate the output by adding the corresponding outputs of f and g. Understanding this concept is crucial for graphing the resulting function.

Graphing Functions

Graphing functions requires plotting points on a coordinate plane based on the function's output values for given input values. For the functions f and g, you will plot their individual graphs and then combine their outputs to create the graph of f + g. This visual representation helps in understanding how the functions interact.

Piecewise Functions

Piecewise functions are defined by different expressions based on the input value. In the context of the given graphs, both f(x) and g(x) may have different linear segments, making them piecewise. When adding these functions, it is important to consider the segments where each function is defined to accurately graph the sum.