📚 Topic Summary
The leading term of a polynomial is the term with the highest degree. When testing for end behavior, the leading term dictates what happens to the function as $x$ approaches positive or negative infinity. Understanding this helps predict the graph's behavior. This worksheet will provide practice in identifying and using the leading term.
Let's dive into some practice problems to solidify your understanding!
🧠 Part A: Vocabulary
Match the term with its definition:
- 📏 Leading Coefficient
- 🧮 Degree of a Polynomial
- 📈 End Behavior
- 📊 Polynomial Function
- ➗ Term
- A function that involves only non-negative integer powers or only positive integer exponents of a variable.
- The behavior of the graph of a function as x approaches positive infinity (+∞) or negative infinity (-∞).
- A number or variable multiplied together.
- The coefficient of the term with the highest degree in a polynomial.
- The highest power of the variable in the polynomial.
✍️ Part B: Fill in the Blanks
Complete the following sentences:
- The ___________ term determines the end behavior of a polynomial.
- The degree of the polynomial $f(x) = 3x^4 - 2x^2 + 7$ is __________.
- If the leading coefficient is positive and the degree is even, the end behavior is: as $x \rightarrow -\infty$, $f(x) \rightarrow \infty$ and as $x \rightarrow \infty$, $f(x) \rightarrow$ __________.
🤔 Part C: Critical Thinking
Explain how the leading term test can help you quickly sketch the graph of a polynomial function. Provide an example.