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

Verified step by step guidance

1. Identify the given function as a set of ordered pairs: $f=\{(2,5),(3,9),(-1,11),(5,3)\}$.
2. To find $f(2)$, locate the ordered pair where the first element is 2. In this case, it is $(2,5)$.
3. The value of $f(2)$ is the second element of the ordered pair $(2,5)$, which is 5.
4. To find $f(-1)$, locate the ordered pair where the first element is -1. In this case, it is $(-1,11)$.
5. The value of $f(-1)$ is the second element of the ordered pair $(-1,11)$, which is 11.

Key Concepts

Function Definition

A function is a relation that assigns exactly one output for each input from its domain. In this context, the function is represented as a set of ordered pairs, where the first element is the input (or 'x' value) and the second element is the output (or 'y' value). 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), you look for the ordered pair where the first element is 2 and read 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 coordinates in a function, typically written as (x, y). In the given function, each pair indicates a specific relationship between the input (x) and output (y). Recognizing and interpreting these pairs is vital for accurately finding the function values at specified inputs.