Give an example of a rational function equation and a non-rational function equation. In a
2-3 sentences, explain what makes one of the functions rational and the other non-rational

A rational function can be expressed as \( f(x) = \frac{2x^2 + 3x + 1}{x - 2} \), where both the numerator and denominator are polynomials. A non-rational function example is \( g(x) = \sqrt{x} + 1 \), which involves a square root.

The rational function is defined as the ratio of two polynomials, while the non-rational function involves a square root, making it not expressible as a ratio of polynomials.

Would you like further details on rational and non-rational functions? Here are 5 related questions:

1. Can a rational function have square roots in the numerator or denominator?
2. What are the vertical asymptotes of rational functions?
3. How do you simplify a rational function?
4. What makes a function transcendental or algebraic?
5. How do you find the domain of a non-rational function?

**Tip:** Always check for undefined values in the denominator of rational functions to identify their domain.

Give an example of a rational function equation and a non-rational function equation. In a 2-3 sentences, explain what makes one of the functions rational and the other non-rational.

Explore the differences between rational and non-rational functions with examples. Learn how to identify rational functions as ratios of polynomials, and understand why functions involving square roots are considered non-rational. Suitable for students in Grades 9-12.

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