a) Draw an example of a relation that is a function and explain why.
Answer
\(\boxed{\text{The relation defined by the square function is a function because for each input, there is exactly one output. For example, the input 1 maps to the output 1, the input 2 maps to the output 4, and so on. No two inputs map to the same output, so this relation is a function.}}\)
Step 1 ：Draw an example of a relation that is a function. A relation is a function if for every input, there is exactly one output. In other words, no two ordered pairs in the relation have the same first element.
Step 2 ：Consider a simple relation where the input is a number and the output is the square of that number. This is a function because for every input number, there is exactly one output which is the square of the input.
Step 3 ：Define the inputs and outputs as follows: inputs = [1, 2, 3, 4, 5], outputs = [1, 4, 9, 16, 25].
Step 4 ：\(\boxed{\text{The relation defined by the square function is a function because for each input, there is exactly one output. For example, the input 1 maps to the output 1, the input 2 maps to the output 4, and so on. No two inputs map to the same output, so this relation is a function.}}\)
