Graphing Rational Functions and Asymptotes

The video tutorial covers graphing rational functions and their asymptotes. It explains the concept of rational functions as quotients of polynomials and discusses the challenges in graphing them due to domain restrictions. The tutorial demonstrates graphing the function 1/X, highlighting vertical and horizontal asymptotes. It provides methods to find these asymptotes by analyzing the function's numerator and denominator. The video also explores graphing techniques, including testing values and using transformations, to understand the behavior of rational functions as they approach asymptotes.

What is a rational function?

• A function that is expressed as a quotient of polynomial functions.

• A function that is expressed as a product of polynomial functions.

• A function that is expressed as a sum of polynomial functions.

• A function that is expressed as a difference of polynomial functions.

Why is the domain of a rational function typically not all real numbers?

• Because the function can be undefined.

• Because the function can be infinite.

• Because the denominator can be zero.

• Because the numerator can be zero.

What happens to the function one over X as X approaches zero from the negative side?

• The function remains constant.

• The function approaches zero.

• The function approaches negative infinity.

• The function approaches positive infinity.

What are the asymptotes of the function one over X?

• X equals zero and Y equals zero.

• X equals infinity and Y equals infinity.

• X equals one and Y equals one.

• X equals negative one and Y equals negative one.

How do you find vertical asymptotes of a rational function?

• By finding the leading coefficient.

• By finding the highest degree term.

• By finding the zeroes of the denominator.

• By finding the zeroes of the numerator.

What is the maximum number of horizontal asymptotes a rational function can have?

• Three

• One

• Two

• Zero

If the degree of the numerator is higher than the degree of the denominator, what can be said about the horizontal asymptote?

• Y equals zero is the asymptote.

• There is no horizontal asymptote.

• Y equals one is the asymptote.

• Y equals infinity is the asymptote.

What does a vertical shift in the function one over X look like?

• A vertical stretch.

• A horizontal shift.

• A vertical shift.

• A horizontal stretch.

What is the effect of having a number within the denominator of one over X?

• It causes a vertical shift.

• It causes a horizontal shift.

• It causes a vertical stretch.

• It causes a horizontal stretch.

What is a useful strategy for graphing rational functions when transformations do not apply?

• Finding vertical asymptotes by identifying the zeroes of the numerator.

• Finding horizontal asymptotes by identifying the zeroes of the denominator.

• Finding vertical asymptotes by identifying the zeroes of the denominator.

• Finding horizontal asymptotes by identifying the zeroes of the numerator.