📚 Topic Summary
When dealing with functions, we can perform basic arithmetic operations like addition, subtraction, multiplication, and division, just like with numbers. The key is to understand that we're operating on the function's output for a given input. So, for two functions $f(x)$ and $g(x)$, $(f+g)(x) = f(x) + g(x)$, $(f-g)(x) = f(x) - g(x)$, $(f\cdot g)(x) = f(x) \cdot g(x)$, and $(f/g)(x) = f(x) / g(x)$, provided $g(x) \neq 0$. Remember to pay attention to the domain of the resulting function, especially in the case of division!
🧠 Part A: Vocabulary
Match the term with its correct definition:
| Term |
Definition |
| 1. Domain |
A. A function resulting from multiplying two functions. |
| 2. Quotient Function |
B. A function resulting from subtracting one function from another. |
| 3. Sum Function |
C. The set of all possible input values for which a function is defined. |
| 4. Difference Function |
D. A function resulting from adding two functions. |
| 5. Product Function |
E. A function resulting from dividing one function by another. |
Answers: 1-C, 2-E, 3-D, 4-B, 5-A
✍️ Part B: Fill in the Blanks
Complete the following sentences using the correct terms.
When you divide two functions, the resulting function is called the __________ function. The __________ of a function is the set of all possible input values. To find the __________ function, you simply add the outputs of two functions together. When creating a __________ function, remember to exclude any x-values that make the denominator zero. The __________ function is obtained by multiplying two functions.
Answers: quotient, domain, sum, quotient, product
🤔 Part C: Critical Thinking
Explain why it's important to consider the domain when adding, subtracting, multiplying, or dividing functions. Give an example to illustrate your point.
