1. Let's start by understanding what a function is: a function is a rule that assigns each input exactly one output. 2. The **domain** of a function is the set of all possible input values (usually $x$) that the function can accept without causing any problems like division by zero or taking the square root of a negative number. 3. The **range** of a function is the set of all possible output values (usually $y$) that the function can produce from the domain. 4. To find the domain, look for values of $x$ that make the function undefined. For example, if the function has a denominator, set it not equal to zero and solve. 5. To find the range, think about all the possible $y$ values the function can take when $x$ moves through the domain. 6. Example: For $f(x) = \sqrt{x}$, the domain is all $x \geq 0$ because you cannot take the square root of a negative number. 7. The range of $f(x) = \sqrt{x}$ is all $y \geq 0$ because square roots are always non-negative. 8. Flashcard idea for domain: "What values can $x$ take in the function?" 9. Flashcard idea for range: "What values can $y$ take as outputs of the function?" 10. Remember, domain is about inputs, range is about outputs. This explanation is a good start for your flashcards on domain and range!