Exploring Rational Functions and Their End Behavior

What is a rational function?

• A function that involves the square root of a polynomial

• A function that involves only multiplication

• A function that involves the division of two polynomials

• A function that involves only addition and subtraction

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

• x^3 - 2x + 1

• x^2 + 3x + 2

• sqrt(x)

• 1/x

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

• Because it would make the function undefined

• Because it would make the function equal to zero

• Because it would make the function a constant

• Because it would make the function a polynomial

How do you determine the domain of a rational function?

• By finding where both the numerator and denominator are zero

• By finding where the denominator is zero

• By finding where the numerator is zero

• By finding where the function is positive

What is interval notation used for in the context of rational functions?

• To express the range of the function

• To express the domain of the function

• To express the zeros of the function

• To express the asymptotes of the function

What are asymptotes in the context of rational functions?

• Lines that the graph of the function crosses

• Points where the function is zero

• Lines that the graph of the function approaches but never touches

• Points where the function is undefined

How do you find the domain of a rational function algebraically?

• By setting the denominator equal to zero

• By setting the numerator equal to zero

• By setting both the numerator and denominator equal to zero

• By finding the derivative of the function

What happens to the value of a rational function as x approaches infinity?

• It approaches zero

• It approaches infinity

• It approaches a constant value

• It oscillates

What is the horizontal asymptote of a rational function?

• A line that the graph approaches as x approaches infinity or negative infinity

• A line that the graph crosses at x = 0

• A point where the function is undefined

• A line that the graph never approaches

What is the significance of the limit of a rational function as x approaches infinity?

• It determines the horizontal asymptote

• It determines the vertical asymptote

• It determines the zeros of the function

• It determines the domain of the function