Rational Function Applications Practice Quiz Algebra 2

📚 Topic Summary

Rational functions are fractions where the numerator and denominator are polynomials. Applications of rational functions pop up everywhere, especially when dealing with rates, mixtures, or inverse relationships. This quiz helps you practice setting up and solving problems where rational functions model the situation. Remember to pay attention to units and check for extraneous solutions!

🧮 Part A: Vocabulary

Match the term with its definition:

1. Term: Asymptote
2. Term: Extraneous Solution
3. Term: Rational Function
4. Term: Rate
5. Term: Inverse Variation

1. A function that can be written as a ratio of two polynomials.
2. A line that a graph approaches but does not touch.
3. A solution that arises from the process of solving an equation but is not a valid solution to the original problem.
4. A relationship where one variable increases as the other decreases, and vice versa.
5. A ratio that compares two different quantities.

✍️ Part B: Fill in the Blanks

When solving word problems involving rational functions, it's important to define your ______ carefully. If you're working with a problem involving combined work rates, remember that the sum of the individual rates equals the ______ rate. Also, don't forget to check for ______ solutions, which can arise when you square both sides of an equation or multiply by an expression containing a variable.

🤔 Part C: Critical Thinking

Describe a real-world situation (other than work-rate problems) that can be modeled using a rational function. Explain which quantities would be represented by the numerator and denominator.