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Chapter 2: Problem 112

What is a rational function?

Short Answer

Expert verified
A rational function is a function which is the ratio of two polynomials.

Step by step solution

01

Define a Polynomial

A polynomial is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. For instance, \(f(x) = 2x^3 - 3x^2 + 4x - 1\) is a polynomial.
02

Define a Rational Number

A rational number is a number that can be expressed as a fraction \(\frac{a}{b}\), where \(a\) and \(b\) are integers and \(b\) is not equal to 0.
03

Define a Rational Function

A rational function is a function which is the ratio of two polynomials. It is of the form \(R(x) = \frac{P(x)}{Q(x)}\), where \(P(x)\) and \(Q(x)\) are polynomials and \(Q(x)\) is not zero.

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Most popular questions from this chapter

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I began the solution of the rational inequality \(\frac{x+1}{x+3} \geq 2\) by setting both \(x+1\) and \(x+3\) equal to zero.

a. If \(y=\frac{k}{x},\) find the value of \(k\) using \(x=8\) and \(y=12\). b. Substitute the value for \(k\) into \(y=\frac{k}{x}\) and write the resulting equation. c. Use the equation from part (b) to find \(y\) when \(x=3\).

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The graph of a rational function can never cross a vertical asymptote.

What is a rational inequality?

Use inspection to describe each inequality's solution set. Do not solve any of the inequalities. $$(x-2)^{2} \leq 0$$
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