Users' questions

What are the transformations of a rational function?

What are the transformations of a rational function?

Any graph of a rational function can be obtained from the reciprocal function f(x)=1x f ( x ) = 1 x by a combination of transformations including a translation, stretches and compressions.

What are the characteristics of rational functions?

A rational function is defined as the quotient of polynomials in which the denominator has a degree of at least 1 . In other words, there must be a variable in the denominator. The general form of a rational function is p(x)q(x) , where p(x) and q(x) are polynomials and q(x)≠0 .

What is a rational function example?

Examples of Rational Functions The function R(x) = (x^2 + 4x – 1) / (3x^2 – 9x + 2) is a rational function since the numerator, x^2 + 4x – 1, is a polynomial and the denominator, 3x^2 – 9x + 2 is also a polynomial.

Do rational functions have End behaviors?

Rational functions often intersect the lines or polynomials that describe their end behavior. When the degree of f(x) is at least two more than the degree of g(x), the rational function will behave like a polynomial.

What are rational functions?

A rational function is one that can be written as a polynomial divided by a polynomial. Since polynomials are defined everywhere, the domain of a rational function is the set of all numbers except the zeros of the denominator. f(x) = x / (x – 3).

How are rational functions used in real life?

Rational functions and equations can be used in many real-life situations. We can use them to describe speed-distance-time relationships and modeling work problems. They can also be used in problems related to mixing two or more substances.

What are the 5 examples of rational function?

Rational Functions

  • f(x)=x+2x.
  • g(x)=x−1x−2.
  • h(x)=x(x−1)(x+5)
  • k(x)=x2−1×2−9.
  • l(x)=x2−1×2+1.

How do you describe the end behavior of a rational function?

Determining the End Behavior of a Rational Function If the degree of the denominator is larger than the degree of the numerator, there is a horizontal asymptote of y=0 , which is the end behavior of the function. Then y=q(x) y = q ( x ) , where q(x) is the quotient that provides the end behavior.

What is the most distinct characteristic of a rational function Brainly?

Answer: Two important features of any rational function r(x)=p(x)q(x) r ( x ) = p ( x ) q ( x ) are any zeros and vertical asymptotes the function may have. These aspects of a rational function are closely connected to where the numerator and denominator, respectively, are zero.