Rational functions practice problems

📚 Topic Summary

Rational functions are simply ratios of two polynomials. They can look intimidating, but with practice, you'll become a pro at manipulating them! The general form of a rational function is $f(x) = \frac{P(x)}{Q(x)}$, where $P(x)$ and $Q(x)$ are polynomials. Important aspects include finding the domain (where $Q(x) \neq 0$), identifying asymptotes, and simplifying the function.

Understanding rational functions is key to many areas of math and science, from calculus to physics. This worksheet will help you solidify your understanding!

🧠 Part A: Vocabulary

Match the term with its definition:

Term	Definition
1. Asymptote	A. A value that makes the denominator of a rational function equal to zero.
2. Domain	B. A line that a graph approaches but never touches.
3. Rational Function	C. A function that can be written as the ratio of two polynomials.
4. Vertical Asymptote	D. The set of all possible input values (x-values) for which the function is defined.
5. Zero	E. A vertical line where the denominator of the simplified rational function equals zero.

📝 Part B: Fill in the Blanks

Complete the following paragraph using the words provided: polynomial, undefined, horizontal, numerator, denominator.

A rational function is a fraction where both the ________ and ________ are ________. The function is ________ where the denominator equals zero. A ________ asymptote describes the behavior of the function as x approaches positive or negative infinity.

🤔 Part C: Critical Thinking

Explain in your own words why it's important to identify the domain of a rational function. Give a real-world example where understanding the domain of a function is crucial.