Questions: Use the graph to complete the Following. (a) Write the equations for all vertical and horizontal asymptotes. Enter the equations using the "and" button as necessary. Select "None" as necessary. Vertical asymptote(s): Horizontal asymptote(s): (b) Find the domain and range of f. Write each answer as an interval or union of intervals. Domain: Range: (c) Find all x-intercepts and y-intercepts. Check all that apply. x-intercept(s): -3 1 2 None y-intercept(s): 1 0 2 None

Solution Steps

• Vertical asymptotes occur where the function approaches infinity as the input approaches a certain value.
• From the graph, the vertical asymptotes are at \( x = -1 \) and \( x = 1 \).

• Horizontal asymptotes occur where the function approaches a constant value as the input approaches infinity or negative infinity.
• From the graph, the horizontal asymptote is at \( y = 0 \).

• The domain is the set of all possible input values (x-values) for the function.
• The range is the set of all possible output values (y-values) for the function.
• From the graph:
  • The domain is \( (-\infty, -1) \cup (-1, 1) \cup (1, \infty) \).
  • The range is \( (-\infty, 0) \cup (0, \infty) \).

Final Answer