Exploring Asymptotes and Zeros in Rational Functions

The video tutorial covers rational functions, focusing on horizontal and vertical asymptotes, holes, and zeros. It begins with an overview of rational functions and explains how to determine horizontal asymptotes based on the degrees of the numerator and denominator. The tutorial then moves on to factoring, identifying holes, and finding vertical asymptotes and zeros. The session concludes with a summary and encouragement to try another example problem.

What determines the presence of horizontal asymptotes in a rational function?

• The specific values of the zeros in the numerator

• The coefficients of the highest degree terms

• The addition of all terms in the numerator and denominator

• The degree of the polynomial in the numerator and denominator

What is the result when the degree of the numerator is greater than the degree of the denominator?

• Cannot be determined

• One horizontal asymptote

• Multiple horizontal asymptotes

• No horizontal asymptotes

Which factoring technique is applicable for a difference of squares?

• Difference of cubes

• Square root method

• Grouping

• Quadratic formula

What is the significance of factoring in finding the characteristics of a rational function?

• It helps in simplifying the function for easy graphing

• It changes the degree of the function

• It is only used for finding horizontal asymptotes

• It determines the coefficients of the function

How do you find a hole in a rational function?

• Multiplying the numerator by the denominator

• Adding the numerator and denominator

• Finding common factors in the numerator and denominator

• Setting the denominator equal to zero

What happens to the factor that creates a hole in the graph of a rational function?

• It is multiplied by the remaining factors

• It is eliminated from the function

• It is set to zero

• It is squared

What does the presence of a hole in the graph of a rational function indicate?

• An undefined value in the function

• A discontinuity that can be crossed

• A point where the function touches the x-axis

• A vertical asymptote

What indicates the absence of vertical asymptotes in a rational function?

• A higher degree in the numerator than in the denominator

• No factors left in the denominator after simplification

• Equal degrees of numerator and denominator

• A degree of zero in the denominator

How do you find the zeros of a rational function?

• Setting the numerator equal to zero

• Setting the denominator equal to zero

• Multiplying the numerator and denominator

• Adding the numerator to the denominator

What is the outcome when there are no factors left in the denominator after simplification?

• The function becomes a linear equation

• The function has an undefined slope

• There will be no vertical asymptotes

• The graph of the function will touch the y-axis