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 function ƒ as a set of ordered pairs: ƒ = {(2,5),(3,9),(-1,11),(5,3)}. Each pair is in the form (x, y), where x is the input and y is the output.
2. To find ƒ(2), look for the ordered pair where the first element (x) is 2. The corresponding second element (y) will be the value of ƒ(2).
3. To find ƒ(-1), look for the ordered pair where the first element (x) is -1. The corresponding second element (y) will be the value of ƒ(-1).
4. Write down the values you found for ƒ(2) and ƒ(-1) based on the ordered pairs from the function.
5. Verify that the values correspond correctly to the inputs given, ensuring no mistakes in reading the ordered pairs.

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 a function given as ordered pairs, this involves finding 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 helps determine if a function value can be found for a given input, ensuring the input exists in the function's set of ordered pairs.