For each function, find (a) ƒ(2) and (b) ƒ(-1). See Example 7. 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 in each pair is the input (x-value) 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. Identify the corresponding second element in that pair, which represents ƒ(2).
3. To find ƒ(-1), look for the ordered pair where the first element is -1. Identify the corresponding second element in that pair, which represents ƒ(-1).
4. If the input value is not found in the set of ordered pairs, then ƒ at that input is undefined for this function.
5. Write down the values of ƒ(2) and ƒ(-1) based on the pairs found or state that the value is undefined if the input is not present.

Key Concepts

Function as a Set of Ordered Pairs

A function can be represented as a set of ordered pairs where each input (x-value) corresponds to exactly one output (y-value). Understanding this helps in identifying the output value for a given input by locating the pair with the matching first element.

Evaluating a Function at a Given Input

Evaluating a function at a specific input means finding the output value associated with that input. For a function defined by ordered pairs, this involves searching the set for the pair whose first element matches the input and then reading off the second element.

Domain and Range of a Function

The domain is the set of all possible input values for a function, while the range is the set of all possible outputs. Knowing the domain helps determine if a function value can be found for a given input, such as checking if 2 or -1 is in the domain before evaluation.