Write a rational function as a reciprocal function then find intercepts and asymptotes

The video tutorial covers the concepts of vertical and horizontal asymptotes in rational functions. It explains how to find X and Y intercepts, determine vertical asymptotes by setting the denominator to zero, and addresses the complexity of finding horizontal asymptotes. The tutorial also revisits polynomial division to aid in understanding horizontal asymptotes and discusses graph transformations. Key takeaways include the importance of not giving up on problems and using known methods to solve them.

What is the x-intercept of a rational function determined by?

• Setting the numerator to zero

• Plugging zero into the function

• Finding the slope of the function

• Setting the denominator to zero

How do you find the vertical asymptotes of a rational function?

• By setting the numerator to zero

• By finding the slope of the function

• By using polynomial division

• By identifying values that make the denominator zero

What is the purpose of using polynomial division in the context of rational functions?

• To handle remainders and understand the quotient

• To determine the y-intercept

• To simplify the function

• To find the x-intercept

What does the quotient represent in polynomial division?

• The remainder of the division

• The original function

• The slope of the function

• The result of the division plus the remainder over the divisor

How does a horizontal asymptote shift when the graph is transformed?

• It shifts left by 2 units

• It moves up by 2 units

• It remains unchanged

• It shifts down by 2 units

What is the new horizontal asymptote if the graph is shifted down by 2 units?

• y = -2

• y = 2

• y = 0

• y = -1

Where does the value -2 appear in the context of the original function?

• As a transformation inside the function

• As a transformation outside the function

• In the numerator

• In the denominator