📚 Topic Summary
In calculus, a function is a relation between a set of inputs (the domain) and a set of permissible outputs (the range) with the property that each input is related to exactly one output. Think of it as a machine: you put something in (from the domain), and it gives you something out (in the range). The domain is the set of all possible input values for which the function is defined, and the range is the set of all possible output values the function can produce. Understanding these concepts is crucial for working with more complex calculus problems.
This worksheet will help you practice identifying these key components of functions.
🧮 Part A: Vocabulary
Match the term with its correct definition:
| Term |
Definition |
| 1. Domain |
A. The set of all possible output values of a function. |
| 2. Range |
B. A relation where each input has only one output. |
| 3. Function |
C. A value that, when input into a function, results in an output of zero. |
| 4. Zero of a Function |
D. A point where a function intersects the y-axis. |
| 5. Y-intercept |
E. The set of all possible input values for a function. |
Match the numbers to the letters (e.g., 1-A, 2-B).
✍️ Part B: Fill in the Blanks
A _______ is a relation where each input corresponds to only one _______. The set of all possible input values is called the _______, while the set of all possible output values is called the _______. To find the domain, consider values that would make the function undefined, such as division by _______ or taking the square root of a negative number.
🤔 Part C: Critical Thinking
Explain, in your own words, why understanding the domain of a function is important in real-world applications. Give an example.