Final answer:
To discern vertical asymptotes, horizontal asymptotes, and holes in a rational function, the function's numerator and denominator are analyzed. The provided options, however, do not adequately represent all three characteristics comprehensively, as they lack clear information about the rational function's actual equation.
Step-by-step explanation:
To identify the vertical asymptotes, horizontal asymptotes, and holes of a rational function, we examine the function's denominator and numerator. Vertical asymptotes occur where the denominator is equal to zero, as long as those values do not also cancel out with factors in the numerator. Horizontal asymptotes depend on the degrees of the polynomials in the numerator and the denominator. Holes in the graph are points where both the numerator and the denominator are zero, which indicates a common factor that can be canceled, leaving a 'hole' in the graph at that x-value.
Given the options:
- A) This option suggests the second blank represents vertical asymptotes, and the third blank represents potential holes.
- B) This option suggests the second blank represents holes, and the third blank represents vertical asymptotes.
- C) This is an incomplete option lacking horizontal asymptotes or holes.
- D) This option suggests the second blank represents holes, and the third blank represents a horizontal asymptote or vertical asymptote, but it isn't clear.
None of these options comprehensively provide equations for all three: vertical asymptotes, horizontal asymptotes, and holes. The question may be missing necessary information or might be formatted incorrectly, as detailed explanations for these aspects are not provided within the options.