Identify asymptotes and intercepts of a rational function

The video tutorial covers rational expressions, focusing on factorability, vertical and horizontal asymptotes, and finding X and Y intercepts. It explains that vertical asymptotes occur when the denominator is zero, but imaginary solutions mean no real vertical asymptotes exist. Horizontal asymptotes are determined by comparing the degrees of the numerator and denominator. The tutorial also provides methods for finding X and Y intercepts, emphasizing the importance of setting the numerator to zero for X intercepts and substituting zero for X to find Y intercepts.

What is the condition for a vertical asymptote to exist in a rational expression?

• The numerator must be zero.

• The expression must be factorable.

• The denominator must be zero.

• Both numerator and denominator must be zero.

How do you determine the horizontal asymptote of a rational expression when the degrees of the numerator and denominator are the same?

• Set the numerator equal to zero.

• Divide the leading coefficients.

• Subtract the degrees of the numerator and denominator.

• Set the denominator equal to zero.

When does a slant asymptote occur in a rational expression?

• When the denominator is zero.

• When the numerator is zero.

• When there is no horizontal asymptote.

• When the degrees of the numerator and denominator are equal.

What is the process to find the x-intercepts of a rational expression?

• Substitute zero for x in the expression.

• Set the denominator equal to zero.

• Set both numerator and denominator equal to zero.

• Set the numerator equal to zero.

How do you find the y-intercept of a rational expression?

• Substitute zero for x in the expression.

• Set the denominator equal to zero.

• Divide the leading coefficients.

• Set the numerator equal to zero.