Use the graph of y = ƒ(x) to find each function value: (a) ƒ(-2) (b) ƒ(0) (c) ƒ(1) and (d) ƒ(4). See Example 7(d).

Verified step by step guidance

1. Step 1: Understand the problem. You are given a function y = ƒ(x) and need to find the values of the function at specific x-values: -2, 0, 1, and 4.
2. Step 2: Locate the graph of y = ƒ(x). This graph will show you the relationship between x and y values.
3. Step 3: For each x-value given in the problem, find the corresponding y-value on the graph.
4. Step 4: Specifically, look at the points on the graph where x = -2, x = 0, x = 1, and x = 4. The y-values at these points are ƒ(-2), ƒ(0), ƒ(1), and ƒ(4) respectively.
5. Step 5: Record the y-values you find for each x-value. These are the function values you are asked to determine.

Key Concepts

Function Evaluation

Function evaluation involves substituting a specific input value into a function to determine its output. For example, to find ƒ(-2), you would locate -2 on the x-axis of the graph and identify the corresponding y-value. This process is fundamental in understanding how functions behave at different points.

Graph Interpretation

Graph interpretation is the ability to read and analyze the information presented in a graph. This includes understanding the axes, identifying key points, and recognizing trends. In this context, it is essential to accurately extract function values from the graph of y = ƒ(x) for the specified inputs.

Coordinate System

A coordinate system provides a framework for locating points in a two-dimensional space using ordered pairs (x, y). The x-axis represents the input values, while the y-axis represents the output values of the function. Understanding this system is crucial for accurately determining function values from a graph.