Identify each of the following functions as polynomial, rational, algebraic, or transcendental f(x)=(2x^3+3x)/(9-7x^2)

Rational functions
asked 2020-11-05
Identify each of the following functions as polynomial, rational, algebraic, or transcendental

Answers (1)

If a function can be defined by a rational fraction i.e. an algebraic fraction such that both the numerator and the denominator are polynomials then it is called ration function.
The given function has polynomial in numerator and denominator both, so this function is a rational function
Answer: Rational function

Relevant Questions

asked 2020-11-06
Are all polynomials rational functions? Are all algebraic functions polynomials?
asked 2020-11-08
Use the Rational Zero Theorem to list all possible rational zeros for the function \(f(x) = x^3 + x^2 - 4x - 4\).
asked 2020-10-20
The function \(\displaystyle{f{{\left({x}\right)}}}={x}\frac{{\left({64}-{x}^{{2}}\right)}^{{1}}}{{2}}\) satisfies the hypotheses of Rolle's Theorem on the interval [-8,8]. Find all values of that satisfy the conclusion of the theorem.
a.) + 1, AND -1
b.) \(\displaystyle+{4}\sqrt{{{2}}}{\quad\text{and}\quad}-{4}\sqrt{{{2}}}\)
c.) \(\displaystyle{4}\sqrt{{{2}}}\)
d.) 1
My answer. The intervals do match and equal zero so Rolles theorem can work.
Second I found the derivative maybe thats where I can't solve this problem.
The derivative that I got was \(\displaystyle{64}-{x}^{{2}}+\frac{{x}}{\sqrt{{{64}-{x}^{{2}}}}}\) maybe i did wrong on the simplifying. I at least tried hopefully some one can explain as much as possible with every single step because I can figure out the algebra part.
asked 2020-11-01
7. Which of the following imply that the real number x must be rational? I. x, x7are both rational II. x, x are both rational II. x5, x are both rational
O I, Il only
O I, IlIl only
O II, Il only
O Il only
O None of these combinations Tagged in
asked 2021-02-12
What are the Limits at Infinity of Rational Functions?
asked 2021-02-11
Construct a rational function that has a vertical asymptote at \(x = 3\) and a removable discontinuity at \(x = -2\).
Explain how you determined your answer.
asked 2020-12-28
Let \(\displaystyle{f{{\left({x}\right)}}}={2}{x}-{3}{\quad\text{and}\quad}{g{{\left({x}\right)}}}={4}{x},{f}\in{d}{\left({f}{o}{g}\right)}{\left({x}\right)}\)
asked 2021-02-21
Form a polynomial function whose real zeros and degree are given. Answers will vary depending on the choice of a leading coefficient. Zeros: -1, multiplicity 1, 3, multiplicity 2, degree 3
asked 2021-03-06
Construct a rational function whose domain is all real numbers. Provide evidence as to why the domain of your rational function is all real numbers.
asked 2020-11-01
Explain how the sets of numbers (counting, whole, integer, rational, irrationals, reals) are related to each other.