Use the graph to evaluate each expression. See Example 3(a). (ƒ+g)(0)

Key Concepts

Function Evaluation

Function evaluation involves substituting a specific input value into a function to determine its output. In this case, evaluating (ƒ+g)(0) means finding the values of both functions f(x) and g(x) at x = 0, and then adding those results together. Understanding how to read and interpret function values from a graph is crucial for this process.

Graph Interpretation

Graph interpretation is the ability to analyze and extract information from a visual representation of functions. The graph provided shows two functions, f(x) and g(x), plotted on the same coordinate system. Recognizing the points where these functions intersect the y-axis will help in determining their values at x = 0, which is essential for evaluating (ƒ+g)(0).

Function Addition

Function addition is the process of combining two functions to create a new function, defined as (ƒ+g)(x) = f(x) + g(x). This concept is important for understanding how to compute the value of (ƒ+g)(0) by first evaluating f(0) and g(0) separately, and then summing those results. Mastery of this concept allows for the manipulation and combination of functions in various mathematical contexts.