📚 Topic Summary
In mathematics, a function is like a machine that takes an input, does something to it, and gives you an output. For every input, you only get one output. Think of a vending machine: you put in money (input), and you get a specific snack (output). It wouldn't make sense if putting in the same amount of money sometimes gave you chips and sometimes chocolate!
To identify functions from tables, graphs, or mappings, check if each input (usually 'x') has only one corresponding output (usually 'y'). If it does, it's a function! If an 'x' value leads to multiple 'y' values, it's not a function.
🧮 Part A: Vocabulary
Match the terms with their definitions. Write the correct letter in the space provided.
| Term |
Definition |
| 1. Function |
a. A set of ordered pairs |
| 2. Relation |
b. The set of all possible output values |
| 3. Domain |
c. A relation where each input has only one output |
| 4. Range |
d. The set of all possible input values |
| 5. Vertical Line Test |
e. A visual test to see if a graph represents a function |
✍️ Part B: Fill in the Blanks
Complete the following sentences using the words provided: input, output, function, relation, domain.
A ________ is a special type of ________ where each ________ has only one ________. The set of all possible inputs is called the ________ of the function.
🤔 Part C: Critical Thinking
Explain, in your own words, why the vertical line test works for identifying functions on a graph. Provide an example of a graph that passes the test and one that fails.