📚 Topic Summary
In mathematics, a function is a relation between a set of inputs (called the domain) and a set of permissible outputs (called the range) with the property that each input is related to exactly one output. We can represent functions using tables of values or ordered pairs. When examining a table or set of ordered pairs, look to see if any input (x-value) is associated with more than one output (y-value). If so, it is not a function! Let's practice!
🧠 Part A: Vocabulary
Match the term with its definition:
- Term: Domain
- Term: Range
- Term: Function
- Term: Ordered Pair
- Term: Relation
- Definition: A set of ordered pairs.
- Definition: A set of all possible output values.
- Definition: A set of all possible input values.
- Definition: A relationship where each input has only one output.
- Definition: A pair of elements written in a specific order (x, y).
✍️ Part B: Fill in the Blanks
A ________ is a relationship where each input has only one ________. The set of all possible inputs is called the ________, and the set of all possible outputs is called the ________. An ________ is a pair of elements written in a specific order.
🤔 Part C: Critical Thinking
Explain, in your own words, why it is important that each input in a function has only one output. What problems might arise if an input had multiple outputs?