How to make sense of a horizontal asymptote

The video tutorial covers rational functions, focusing on finding X and Y intercepts, vertical and horizontal asymptotes, and transformations. It explains division and remainders in rational functions, emphasizing the importance of recognizing patterns and transformations. The tutorial provides a comprehensive understanding of these concepts, aiding students in solving related problems effectively.

What is the X intercept of a rational function?

• The value of Y when X is zero

• The point where the graph is undefined

• The point where the graph crosses the Y-axis

• The value of X when Y is zero

How do you find the Y intercept of a rational function?

• Set the denominator to zero

• Evaluate the function at X equals zero

• Find where the graph crosses the X-axis

• Set the numerator to zero

What causes a vertical asymptote in a rational function?

• The denominator equals zero

• The graph crosses the X-axis

• The numerator equals zero

• The function is undefined

What is the significance of the degree of the numerator and denominator in finding horizontal asymptotes?

• It affects the vertical asymptote

• It determines the X intercept

• It determines the Y intercept

• It helps find the horizontal asymptote

What is the purpose of dividing polynomials in the context of rational functions?

• To determine horizontal asymptotes

• To find the Y intercept

• To find the X intercept

• To simplify the function

How is the remainder used when dividing polynomials?

• It is ignored

• It is added to the quotient

• It determines the vertical asymptote

• It is subtracted from the quotient

What transformation occurs when a rational function is written in reciprocal form?

• Horizontal shift

• Reflection

• Rotation

• Vertical shift