For each function, find (a) ƒ(2) and (b) ƒ(-1). See Example 7. ƒ = {(2, 5), (3, 9), (-1, 11), (5, 3)}

Key Concepts

Function Definition

A function is a relation that assigns exactly one output for each input from a given set. In this context, the function ƒ is represented as a set of ordered pairs, where the first element is the input (domain) and the second element is the output (range). Understanding this definition is crucial for determining the outputs for specific inputs.

Evaluating Functions

Evaluating a function involves substituting a specific input value into the function to find the corresponding output. For example, to find ƒ(2), one must look for the ordered pair in the function where the first element is 2 and then identify the second element as the output. This process is essential for solving the given problem.

Ordered Pairs

Ordered pairs are pairs of numbers that represent a point in a two-dimensional space, where the first number indicates the x-coordinate (input) and the second number indicates the y-coordinate (output). In the function ƒ, each ordered pair provides a direct mapping from an input to its output, which is fundamental for evaluating the function at specific values.