Use the graph to evaluate each expression. See Example 3(a).
(ƒ+g)(2)

Verified step by step guidance

1. Identify the value of x for which you need to evaluate the expression. Here, it is x = 2.
2. Locate x = 2 on the horizontal axis (x-axis) of the graph.
3. Find the corresponding y-values for both functions f(x) and g(x) at x = 2 by looking at the points on the orange curve (f) and the blue line (g).
4. Write down the values: f(2) and g(2) from the graph.
5. Add the two values together to find (f + g)(2) using the formula: \[(f + g)(2) = f(2) + g(2)\].

Key Concepts

Function Notation and Evaluation

Function notation, such as f(x) and g(x), represents the output of a function for a given input x. Evaluating a function at a specific value means finding the corresponding y-value on the graph or from the function's equation. For example, f(2) is the y-value of function f when x = 2.

Function Addition (ƒ + g)(x)

The sum of two functions, (ƒ + g)(x), is found by adding their outputs for the same input x. This means (ƒ + g)(2) = f(2) + g(2). Understanding this concept allows you to combine values from two different functions at a specific point.

Reading Values from a Graph

To evaluate functions using a graph, locate the input value on the x-axis, then find the corresponding y-values on each function's curve. Accurate reading of these points is essential for correctly evaluating expressions like (ƒ + g)(2) by summing the y-values of f and g at x = 2.