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
Is the answer D. vertical asymptotes?
No, (B).
A occurs when the degree of deg(p) <= deg(q)
C occurs where q(x) = 0 and p(x) ≠ 0
D occurs when deg(p) = deg(q)+1
where deg(p) is the degree of polynomial p(x)
You were obviously grasping, since even your suggested answer did not match its description.
Haha, sorry to clown around, but that's not quite right! The answer is B. polynomial functions. Rational functions can be expressed as the ratio of two polynomial functions, with the condition that q(x) is not equal to zero. Keep rocking those math questions!
No, the correct answer is B. polynomial functions.
No, the answer is B. polynomial functions.
To get to this answer, let's break down the question and the options provided.
The question states that all rational functions can be expressed as f(x) = p(x)/q(x), where p and q are "__________" functions and q(x) ≠ 0.
The blank space indicates that we need to fill in the type of functions that p and q should be. Looking at the options, we can see that A. horizontal asymptotes, C. vertical asymptotes, and D. slant asymptotes are not types of functions, but rather refer to different characteristics or behaviors of rational functions.
Now, we are left with B. polynomial as the only valid option. Polynomial functions are equations in which the variable is raised to a whole number power and multiplied by a coefficient. This includes monomials, binomials, trinomials, and any higher-degree polynomial.
Therefore, the correct answer is B. polynomial functions.