Use the graph of g to solve Exercises 71–76.

Find g(2)

Verified step by step guidance

1. Step 1: Understand the problem. The goal is to find g(2), which means determining the value of the function g at x = 2. This involves locating the point on the graph where x = 2 and identifying the corresponding y-coordinate.
2. Step 2: Locate x = 2 on the graph. On the horizontal axis (x-axis), find the point where x equals 2.
3. Step 3: Trace vertically from x = 2 to the graph of the function g. Move upward or downward along the vertical line at x = 2 until you intersect the red curve representing the function g.
4. Step 4: Identify the y-coordinate of the intersection point. The y-coordinate of this point is the value of g(2).
5. Step 5: Verify the result visually. Ensure that the intersection point corresponds to x = 2 and confirm the y-coordinate by checking the graph's scale.

Key Concepts

Function Notation

Function notation, such as g(x), is a way to represent a function's output based on its input. In this case, g(2) refers to the value of the function g when the input is 2. Understanding function notation is essential for interpreting and solving problems involving functions.

Graph Interpretation

Interpreting a graph involves analyzing the visual representation of a function to extract information about its behavior. For example, to find g(2), one must locate the point on the graph where x equals 2 and read the corresponding y-value. This skill is crucial for solving problems that require understanding the relationship between variables.

Coordinate System

A coordinate system, typically a Cartesian plane, consists of two perpendicular axes: the x-axis (horizontal) and the y-axis (vertical). Each point on the graph is defined by an ordered pair (x, y). Familiarity with the coordinate system is necessary for accurately locating points and understanding the function's behavior across different values.