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The activity in the image asks to determine whether the given expressions are a rational function, rational equation, rational inequality, or none of these. You are also asked to state your reason.

Let’s analyze the expressions:

1. \( 1 + x = 4 \)

   - This is a **rational equation**, because it is an equation involving rational numbers or variables in a linear form (no division by a variable involved).

2. \( \frac{5x}{2x-1} > 2 \)

   - This is a **rational inequality**, because it involves a rational expression (a fraction with a variable in the denominator) and an inequality symbol.

3. \( f(x) = \frac{x^2 + 7}{x + 2} - 3 \)

   - This is a **rational function**, because it represents a function where the output is a rational expression, meaning a fraction in which the numerator and denominator are polynomials.

4. \( \frac{y+2}{x-2} = y + 3 \)

   - This is a **rational equation**, because it involves an equation with rational expressions (fractions) containing variables.

5. \( \frac{\sqrt{y+5}}{y} = 2 \)

   - This is **none of these** because it involves a square root, which disqualifies it from being classified as a rational equation or rational function.

Would you like further clarification on any of these? Here are 5 related questions for further practice:

1. How do you identify a rational function from a given equation?
2. What differentiates a rational equation from a rational inequality?
3. Can a rational function contain square roots? Why or why not?
4. How do the domains of rational functions differ from regular polynomial functions?
5. How do you solve a rational inequality involving multiple terms?

**Tip:** Remember, for rational expressions, the denominator must never be zero—this helps in determining the domain or solving for exclusions.

Determine whether the given is a rational function, rational equation, rational inequality, or none of these. And state your reason. The given expressions are:
1. 1 + x = 4
2. 5x / (2x - 1) > 2
3. f(x) = (x^2 + 7) / (x + 2) - 3
4. (y + 2) / (x - 2) = y + 3
5. sqrt(y + 5) / y = 2

Learn how to identify whether an expression is a rational function, rational equation, rational inequality, or none of these with a detailed explanation. This problem covers key mathematical concepts such as rational expressions, inequalities, and domain restrictions. Suitable for Grades 10-12 students.

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