Find the Slant Asymptotes x and y intercepts of rational function

The video tutorial covers the identification of horizontal and vertical asymptotes, including potential holes in functions. It explains the concept of oblique asymptotes through long division and highlights the importance of the quotient in determining them. The tutorial also addresses how to find X and Y intercepts and why remainders are not needed in certain calculations.

What is the first step in identifying a vertical asymptote?

• Set the numerator equal to zero.

• Check for a horizontal asymptote.

• Find the derivative of the function.

• Set the denominator equal to zero.

What is an oblique asymptote?

• A line that the graph approaches horizontally.

• A line that the graph approaches at an angle.

• A line that the graph approaches vertically.

• A point where the graph intersects the axis.

How is the oblique asymptote determined?

• By setting the numerator equal to zero.

• By finding the intersection of the graph with the axes.

• By finding the remainder of the division.

• By performing long division and using the quotient.

What is the X-intercept of a function?

• The point where the graph has a hole.

• The point where the graph crosses the X-axis.

• The point where the graph has a vertical asymptote.

• The point where the graph crosses the Y-axis.

Why is the remainder not used in finding the oblique asymptote?

• Because it is used to find the Y-intercept.

• Because it is always zero.

• Because it is used to find the X-intercept.

• Because it does not affect the asymptote.