Understanding Rational Functions

The video tutorial explains rational functions, which are defined as the ratio of two polynomial functions, similar to how rational numbers are expressed as P over Q. It emphasizes that the denominator polynomial must not be zero. Examples of rational functions are provided, and the challenges of graphing them are discussed. The tutorial concludes by summarizing the properties and definition of rational functions.

What is a rational function?

• A function that is always linear

• A function that is a ratio of two polynomials

• A function that is always quadratic

• A function that is a sum of two polynomials

Why can't the denominator of a rational function be zero?

• Because it would make the function linear

• Because it would make the function constant

• Because it would make the function undefined

• Because it would make the function quadratic

How is a rational function similar to a rational number?

• Both are always integers

• Both are always positive

• Both are always negative

• Both are in the form of a ratio

In the expression P/Q, what must be true about Q?

• Q must be greater than P

• Q must be less than P

• Q must be zero

• Q must not be zero

Which of the following is an example of a rational function?

• x^3 + 5

• (x^2 + 3)/(x^3 + 5)

• x^2 + 3

• x + 2

What is the numerator in the rational function (x^2 + 3)/(x^3 + 5)?

• x^2 + 3

• x^3 + 5

• x + 5

• x^2 + 5

Why can't we predict the graph of a rational function easily?

• Because it is always linear

• Because it is always quadratic

• Because it is always constant

• Because it depends on the specific polynomials involved

What must be done to understand the behavior of a rational function's graph?

• Calculate and analyze the function

• Guess the shape

• Assume it is linear

• Assume it is quadratic

How is a rational function defined in terms of real numbers?

• As a mapping from real numbers to integers

• As a mapping from integers to real numbers

• As a mapping from integers to integers

• As a mapping from real numbers to real numbers

What is the structure of a rational function?

• A product of two polynomials

• A ratio of two polynomials

• A difference of two polynomials

• A sum of two polynomials