Graph a rational function with vertical and oblique asymptotes

The video tutorial covers the process of graphing rational functions with a focus on identifying and graphing vertical, horizontal, and slant asymptotes. It begins with an introduction to vertical asymptotes, followed by a discussion on horizontal and slant asymptotes. The instructor demonstrates how to use long division to find slant asymptotes and graph them. The tutorial also includes finding X and Y intercepts and discusses the behavior of the graph concerning multiplicity of roots. The session concludes with final graphing steps and a summary of the key points.

What is the first step in finding a vertical asymptote?

• Set the numerator equal to zero.

• Set the denominator equal to zero.

• Use synthetic division.

• Find the degree of the polynomial.

When is there no horizontal asymptote?

• When the degree of the numerator is equal to the denominator.

• When the polynomial is linear.

• When the degree of the numerator is less than the denominator.

• When the degree of the numerator is greater than the denominator.

What is a requirement for using synthetic division?

• The divisor must be a linear binomial.

• The dividend must be a quadratic polynomial.

• The dividend must be a linear polynomial.

• The divisor must be a quadratic binomial.

What is the purpose of long division in finding slant asymptotes?

• To find the remainder of the division.

• To determine the degree of the polynomial.

• To find the equation of the slant asymptote.

• To simplify the polynomial.

What is the result of dividing a polynomial by a linear binomial?

• A quadratic polynomial.

• A slant asymptote.

• A linear polynomial.

• A constant.

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

• Use synthetic division.

• Set Y to zero and solve for X.

• Set X to zero and solve for Y.

• Find the degree of the polynomial.

How do you determine the X-intercept of a function?

• Set Y to zero and solve for X.

• Set X to zero and solve for Y.

• Find the degree of the polynomial.

• Use long division.

What is the significance of a zero with even multiplicity?

• The graph has a horizontal asymptote.

• The graph touches but does not cross the X-axis.

• The graph crosses the X-axis.

• The graph has a vertical asymptote.

What does the graph of a function with a slant asymptote do?

• Remains parallel to the slant asymptote.

• Crosses the slant asymptote.

• Approaches the slant asymptote as X approaches infinity.

• Has no relation to the slant asymptote.

What happens to the graph at a point of even multiplicity?

• It crosses the axis.

• It touches and rebounds.

• It becomes undefined.

• It forms a cusp.