Question

example of rational function having a denominator only one term​

Answer 1

Step-by-step explanation:

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.

Answer 2

Answer:

A rational function is defined as the quotient of polynomials in which the denominator has a degree of at least 1 . There must be a variable in the denominator.

Step-by-step explanation:

Polynomial is an expression comprising variables and coefficients.

The rational expression is fractions involving polynomials

Polynomial:

a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

An example of a polynomial of a single indeterminate, x, is x² − 4x + 7

Polynomial Functon :

A polynomial function is a function which involves only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, cubic equation

Rational:

The definition of rational is something that makes sense or that could be based in fact or someone who behaves and thinks logically.

Rational Function:

a rational function is any function which can be defined by a rational fraction, i.e. an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rational numbers; they may be taken in any field K.

polynomials are used to describe curves of various types, people use them in the real world to graph curves. For example, roller coaster designers may use polynomials to describe the curves in their rides.

Process for Graphing a Rational Function and Polynomials

1. Find the intercepts, if there are any
2. Find the vertical asymptotes by setting the denominator equal to zero and solving.
3. Find the horizontal asymptote, if it exists, using the fact above
4. The vertical asymptotes will divide the number line into regions
5. Sketch the graph.

Question: Give an example of a rational function that has vertical asymptote x=3 now give an example of one that has vertical asymptote x=3 and horizontal asymptote y=2. Now give an example of a rational function with vertical asymptotes x=1 and x=−1, horizontal asymptote y=0 and x-intercept 4.

• (x−3). This is because when we find vertical asymptote(s) of a function, we find out the value where the denominator is 0 because then the equation will be of a vertical line for its slope will be undefined.
• 2x(x−3). Same reasoning for vertical asymptote, but for horizontal asymptote, when the degree of the denominator and the numerator is the same, we divide the coefficient of the leading term in the numerator with that in the denominator, in this case 21=2
• (x−4)(x−1)(x+1). Same reasoning for vertical asymptote. Horizontal asymptote will be y=0 as the degree of the numerator is less than that of the denominator and x-intercept will be 4 as to get intercept, we have to make y, that is, f(x)=0 and hence, make the numerator 0. So, in this case; to get x-intercept 4, we use (x−4) in the numerator so that (x−4)=0⟹x=4.

Reference link

• https://brainly.in/question/28206699