In Exercises 65–70, use the graph of f to find each indicated function value. f(4)

Verified step by step guidance

1. Step 1: Understand the problem. The goal is to find the value of the function f(x) when x = 4. This means we need to locate the point on the graph of f where the x-coordinate is 4 and determine the corresponding y-coordinate.
2. Step 2: Locate x = 4 on the x-axis of the graph. This is the horizontal axis, and you should find the point where x equals 4.
3. Step 3: From x = 4, move vertically (up or down) until you intersect the graph of the function f. This intersection point represents the value of the function at x = 4.
4. Step 4: Identify the y-coordinate of the intersection point. The y-coordinate of this point is the value of f(4).
5. Step 5: Write down the result as f(4) = [y-coordinate], where [y-coordinate] is the value you found in the previous step.

Key Concepts

Function Notation

Function notation, such as f(x), is a way to denote a function's output for a given input x. In this context, f(4) represents the value of the function f when the input is 4. Understanding function notation is essential for interpreting and evaluating functions correctly.

Graph Interpretation

Interpreting a graph involves analyzing the visual representation of a function to determine its values at specific points. For the question, locating the point on the graph where x equals 4 allows us to find the corresponding y-value, which is f(4). This skill is crucial for understanding how functions behave visually.

Domain and Range

The domain of a function is the set of all possible input values (x-values), while the range is the set of all possible output values (y-values). Knowing the domain and range helps in understanding the limits of the function's inputs and outputs, which is important when evaluating specific function values like f(4).