https://file.aiquickdraw.com/mathbot/file/172602294496834m6omiv.jpg

Let's break down and solve the questions from the image step by step.

### Section A: Classifying functions

You need to classify the functions given based on their degree. The choices are:
1. Linear Function
2. Quadratic Function
3. Cubic Function
4. Quartic Function
5. Quintic Function

The degree of a polynomial function is determined by the highest power of the variable \( x \).

#### Questions:
1. \( 3x^2 - 1 \)
   - The highest degree is 2, so this is a **Quadratic Function**.

2. \( 2x^3 + 4x + 5 \)
   - The highest degree is 3, so this is a **Cubic Function**.

3. \( 4x^4 + 5x^2 + 3x \)
   - The highest degree is 4, so this is a **Quartic Function**.

4. \( x^5 + 3x^2 - 2 \)
   - The highest degree is 5, so this is a **Quintic Function**.

5. \( 5x + 1 \)
   - The highest degree is 1, so this is a **Linear Function**.

### Section B: Identifying laws of exponents

For questions 7 to 10, you need to identify the law of exponents being used. The options provided are:
1. Power rule
2. Quotient rule
3. Negative exponent rule

The exponent laws are:
- **Power rule**: \( (a^m)^n = a^{mn} \)
- **Quotient rule**: \( \frac{a^m}{a^n} = a^{m-n} \)
- **Negative exponent rule**: \( a^{-n} = \frac{1}{a^n} \)

#### Questions:
7. \( \frac{a^m}{b^n} = \frac{a^m}{b^n} \)  
   This uses the **Quotient rule**.

8. Other exponents are not fully visible from the current image, but similar rules will apply. 

---

Let me know if you need further clarifications on any of these or more detailed explanations.

Would you like to explore any specific part of this solution further?

### Related questions:
1. How do you classify higher-order polynomial functions?
2. Can you explain how to simplify polynomials before identifying their degree?
3. How are exponent rules applied when dealing with negative exponents?
4. What are some common applications of quadratic functions?
5. How can you graph each type of polynomial function based on its degree?

### Tip:
When classifying functions, always look for the term with the highest exponent to determine the degree!

Classify the functions based on their degree and identify the laws of exponents being used.

Learn how to classify polynomial functions based on their degree, including linear, quadratic, cubic, quartic, and quintic functions. This problem also covers key laws of exponents, including the power rule, quotient rule, and negative exponent rule. Suitable for students in Grades 7-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation