Transcendental functions are defined as what?

Transcendental functions are defined as what?

• A. All non-algebraic functions, such as logarithms, trigonometric functions, or variables as exponents
• B. Only polynomial functions
• C. Only linear functions
• D. Functions with rational outputs

Answer: (A)

Transcendental functions are those that are not algebraic. In other words, they do not satisfy any polynomial equation with constant coefficients in x, so you can’t express them as a finite polynomial in x or as roots of such polynomials. Classic examples include logarithms, sine and cosine, and exponential functions like e^x. That’s why the description “all non-algebraic functions” best fits: it names the property that defines transcendence, beyond how a function behaves or what its outputs look like.

Transcendental functions are those that are not algebraic. In other words, they do not satisfy any polynomial equation with constant coefficients in x, so you can’t express them as a finite polynomial in x or as roots of such polynomials. Classic examples include logarithms, sine and cosine, and exponential functions like e^x. That’s why the description “all non-algebraic functions” best fits: it names the property that defines transcendence, beyond how a function behaves or what its outputs look like.