To determine whether the statement "If the equation of a function is a rational expression, the function is rational" is true or false, we need to understand the definition of a rational function and a rational expression.
### Definitions
1. Rational Expression: A rational expression is a ratio (or fraction) of two polynomials. Formally, an expression of the form \(\( \frac{P(x)}{Q(x)} \)\), where \(\( P(x) \)\) and \(\( Q(x) \)\) are polynomials, and \(\( Q(x)
eq 0 \)\).
2. Rational Function: A rational function is a function that can be expressed as a ratio of two polynomials. Formally, \(\( f(x) = \frac{P(x)}{Q(x)} \)\), where \(\( P(x) \)\) and \(\( Q(x) \)\) are polynomials, and \(\( Q(x)
eq 0 \)\).
### Explanation
- A rational function, by definition, is any function that can be expressed as the ratio of two polynomials.
- A rational expression is also defined as a ratio of two polynomials.
Since a rational function and a rational expression share the same requirement—they are both ratios of polynomials—it follows that if the equation of a function is a rational expression, then by definition, the function itself is a rational function.
### Conclusion
Given the definitions and the logical equivalence between rational expressions and rational functions, the statement is indeed true.
Answer:
A. True
