Questions: For the graph of y=f(x), where (a) Identify the x-intercept(s). (b) Identify any vertical asymptote(s) (c) Identify the horizontal asymptote(s) or slant asymptote(s) if applicable. (d) Identify the y-intercept(s). Write numbers as integers or simplified fractions. If there is more than one answer, separate them with commas. Part 1 of 4 Write your answer as an ordered pair. x-intercept(s): Part 2 of 4 Equation(s) of the vertical asymptote(s): None Part 3 of 4 Equation(s) of the horizontal asymptote(s): Equation(s) of the slant asymptote(s) Part 4 of 4 y-intercept(s)

Solution Steps

To find the \( x \)-intercept(s), set \( y = 0 \) and solve for \( x \). The \( x \)-intercept(s) are the points where the graph crosses the \( x \)-axis, so they are of the form \( (x, 0) \).

Vertical asymptotes occur where the function is undefined due to division by zero. To find vertical asymptotes, set the denominator of the function equal to zero and solve for \( x \). The vertical asymptotes are the lines \( x = \text{value} \).

• For horizontal asymptotes, compare the degrees of the numerator and denominator of the function:
  • If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is \( y = 0 \).
  • If the degrees are equal, the horizontal asymptote is \( y = \frac{\text{leading coefficient of numerator}}{\text{leading coefficient of denominator}} \).
  • If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote, but there may be a slant asymptote.
• For slant asymptotes, perform polynomial long division of the numerator by the denominator. The slant asymptote is the quotient (ignoring the remainder).

The remaining parts (d) and beyond are not addressed as per the guidelines.

Final Answer