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. Identify the function values you need to find: ƒ(-2), ƒ(0), ƒ(1), and ƒ(4). These represent the y-values of the function at the given x-values.
2. Locate each x-value on the x-axis of the graph of y = ƒ(x). For example, find the point where x = -2 on the horizontal axis.
3. From each x-value, move vertically to the point on the graph of the function. The height of this point corresponds to the function value ƒ(x) at that x.
4. Read the y-coordinate of the point on the graph directly above or below each x-value. This y-coordinate is the value of ƒ(x) you are asked to find.
5. Write down the function values for each x: ƒ(-2), ƒ(0), ƒ(1), and ƒ(4) based on the y-coordinates you identified from the graph.

Key Concepts

Function and Function Notation

A function assigns each input value (x) exactly one output value (y). The notation ƒ(x) represents the output of the function ƒ at input x. Understanding this helps interpret what ƒ(-2), ƒ(0), etc., mean: the y-values corresponding to those x-values on the graph.

Reading Values from a Graph

To find ƒ(x) from a graph, locate the input x on the horizontal axis, then find the corresponding point on the curve. The y-coordinate of this point is the function value ƒ(x). This skill is essential for answering questions about function values using graphical information.

Domain and Range of a Function

The domain is the set of all possible input values (x) for which the function is defined, and the range is the set of all possible output values (y). Knowing the domain ensures the x-values given (like -2, 0, 1, 4) are valid inputs on the graph before finding their corresponding outputs.