For each function, find (a) ƒ(2) and (b) ƒ(-1). ƒ = {(-1,3),(4,7),(0,6),(2,2)}

Verified step by step guidance

1. Understand that the function ƒ is given as a set of ordered pairs, where the first element of each pair is the input (x) and the second element is the output (ƒ(x)).
2. To find ƒ(2), look for the ordered pair where the first element is 2. The second element of that pair will be the value of ƒ(2).
3. To find ƒ(-1), look for the ordered pair where the first element is -1. The second element of that pair will be the value of ƒ(-1).
4. If the input value is not found in the set of ordered pairs, then ƒ at that input is not defined for this function.
5. Write down the values of ƒ(2) and ƒ(-1) based on the ordered pairs you identified.

Key Concepts

Function Notation and Evaluation

Function notation, written as ƒ(x), represents the output value of the function ƒ at the input x. Evaluating ƒ at a specific value means finding the corresponding output from the function's definition or set of ordered pairs.

Ordered Pairs and Domain

A function can be represented as a set of ordered pairs (x, y), where x is an input from the domain and y is the output. Understanding that each x-value corresponds to exactly one y-value is essential for correctly identifying ƒ(2) and ƒ(-1).

Domain and Range Identification

The domain is the set of all possible input values (x-values) for the function, while the range is the set of all output values (y-values). Recognizing which inputs exist in the domain helps determine if ƒ(2) or ƒ(-1) can be found from the given pairs.