https://file.aiquickdraw.com/mathbot/file/1724576448723595x2z27.jpg

To answer the questions on the sheet you provided, I will first classify each expression according to the instructions:

1. **Green** - Rational Function: A function that is the ratio of two polynomials.
2. **Orange** - Rational Equation: An equation that involves rational expressions.
3. **Yellow** - Rational Inequality: An inequality that involves rational expressions.

I'll now go through each expression:

### Row 1:
1. \( y = \frac{1}{x+1} \) - **Green (Rational Function)**
2. \( \frac{x-1}{x+2} > 0 \) - **Yellow (Rational Inequality)**
3. \( 5x = 2 \) - **Orange (Rational Equation)**
4. \( \frac{4x-3}{2x+1} = 0 \) - **Orange (Rational Equation)**

### Row 2:
1. \( y = \frac{2x-1}{x+3} \) - **Green (Rational Function)**
2. \( y = \frac{3x}{2} + 5 \) - **Green (Rational Function)**
3. \( y = \frac{x+1}{x-2} \) - **Green (Rational Function)**
4. \( 5x^2 - 3x = 0 \) - **Orange (Rational Equation)**

### Row 3:
1. \( f(x) = \frac{1}{x} \) - **Green (Rational Function)**
2. \( \frac{3x-5}{x+2} \leq 2 \) - **Yellow (Rational Inequality)**
3. \( \frac{x+1}{x-3} = \frac{2x-1}{x+2} \) - **Orange (Rational Equation)**
4. \( 4x = 3 \) - **Orange (Rational Equation)**

### Row 4:
1. \( y = \frac{3}{x} \) - **Green (Rational Function)**
2. \( 2x + 1 = 0 \) - **Orange (Rational Equation)**
3. \( y = \frac{3x-1}{2x+4} \) - **Green (Rational Function)**
4. \( f(x) = \frac{2}{x} - 5 \) - **Green (Rational Function)**

### Row 5:
1. \( y = 5x + 3 \) - **Green (Rational Function)**
2. \( \frac{3x - 1}{x+5} < 2 \) - **Yellow (Rational Inequality)**
3. \( 2x - 1 = 5 \) - **Orange (Rational Equation)**
4. \( f(x) = \frac{x+1}{2x-3} \) - **Green (Rational Function)**

### Row 6:
1. \( \frac{2x-1}{x+3} \geq 1 \) - **Yellow (Rational Inequality)**
2. \( \frac{3}{x+2} = 2 \) - **Orange (Rational Equation)**
3. \( \frac{2}{x-1} - y = 3 \) - **Orange (Rational Equation)**
4. \( y = \frac{7x}{x+5} \) - **Green (Rational Function)**

### Row 7:
1. \( f(x) = \frac{2x-3}{x+4} \) - **Green (Rational Function)**
2. \( 2x - 3 = 1 \) - **Orange (Rational Equation)**
3. \( \frac{3}{x} \leq 5 \) - **Yellow (Rational Inequality)**
4. \( \frac{4}{x-1} = y \) - **Orange (Rational Equation)**

### Row 8:
1. \( y = 2x + 3 \) - **Green (Rational Function)**
2. \( \frac{2x+1}{x-1} > 3 \) - **Yellow (Rational Inequality)**
3. \( \frac{4}{x+5} = 3 \) - **Orange (Rational Equation)**
4. \( \frac{2x+1}{5} = 1 - y \) - **Orange (Rational Equation)**

If you have any questions or need further clarification on any of the expressions, feel free to ask!

### 5 Relative Questions:
1. What is the general form of a rational function?
2. How can you solve rational inequalities?
3. What are the conditions under which a rational equation has no solution?
4. How can you determine the domain of a rational function?
5. How do you graph a rational function?

### Tip:
When solving rational equations, always check for extraneous solutions that may arise from the restrictions on the variable (like values that make the denominator zero).

Explore how to solve rational functions, equations, and inequalities with a comprehensive guide. This problem set covers key concepts including rational functions, equations, and inequalities. Suitable for advanced high school students preparing for exams.

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