All rational functions can be expressed as f(x) = p(x)/q(x), where p and q are __________ functions and q(x) ≠ 0.
A. horizontal asymptotes
B. polynomial
C. vertical asymptotes
D. slant asymptotes
My answer is B is this correct.
Correct answer.
Well, let's see here. Rational functions can indeed be expressed as f(x) = p(x)/q(x), where p and q are polynomial functions. So, yeah, that seems like the right answer to me! Good job, smarty pants!
Yes, your answer is correct. The expression for a rational function, f(x) = p(x)/q(x), states that p(x) and q(x) are functions. In this case, p(x) and q(x) are polynomial functions, which means that they can be expressed as a sum of terms, each containing a variable raised to a non-negative integer power multiplied by a constant coefficient. It is important to note that in a rational function, q(x) must not be equal to zero, as this would result in an undefined expression. Therefore, option B "polynomial" is the correct answer.
Yes, your answer is correct. The correct answer is B. Polynomial.
To understand why, let's first define what a rational function is. A rational function is a function that can be expressed as the ratio of two polynomials, where the denominator polynomial is not equal to zero.
In this case, the given function f(x) = p(x)/q(x), where p and q are polynomials, represents a rational function. The numerator polynomial p(x) and the denominator polynomial q(x) are required to be polynomials.
The options provided in the question are:
A. Horizontal asymptotes: These are not required for a rational function to be expressed as f(x) = p(x)/q(x). Horizontal asymptotes describe the behavior of a function as x approaches infinity or negative infinity. They are not directly related to the polynomials p(x) and q(x).
C. Vertical asymptotes: These are not required for a rational function to be expressed as f(x) = p(x)/q(x). Vertical asymptotes occur when the denominator polynomial q(x) approaches zero at certain values of x. They are also not directly related to the polynomials p(x) and q(x).
D. Slant asymptotes: Similar to horizontal asymptotes, slant asymptotes describe the behavior of a function as x approaches infinity or negative infinity. They can occur for certain rational functions, but they are not inherent properties of all rational functions.
Therefore, the correct option that describes the requirement for the polynomials in a rational function is B. Polynomial. The numerator p(x) and the denominator q(x) must both be polynomials for a function to be expressed as f(x) = p(x)/q(x), with q(x) ≠ 0.