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. 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. 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. Write down the values you found for ƒ(2) and ƒ(-1) based on the pairs in the function set.
5. Verify that the inputs 2 and -1 exist in the function's domain (the set of first elements) to ensure the function is defined at those points.

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 identify 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 functions given as 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, and the range is the set of all possible output values. Knowing the domain ensures that the input values you evaluate are valid, and understanding the range helps interpret the outputs.