Question

Which equation models the rational function shown in the graph?

Answer 1

I don’t see the graph — could you upload it or describe its key features? Useful details:

- Vertical asymptotes (x = ?). Note if the curve crosses/changes sign at the asymptote (multiplicity odd) or just touches and returns (multiplicity even).
- Holes (point removed) and their x-values.
- x-intercepts (zeros) and whether the graph crosses (odd multiplicity) or touches (even multiplicity).
- Horizontal/oblique asymptote (y = ? or slant).
- A specific point on the graph (for determining leading constant), e.g. f(0) or any labeled point.

If you want to work it out now, here’s the method I’ll use once you give those details:

1. For each vertical asymptote x = a, include factor (x − a)^m in the denominator; choose m = 1 if the graph changes sign across the asymptote (odd), m = 2 if it just touches/turns (even).
2. For each zero (x-intercept) at x = b, include (x − b)^k in the numerator; multiplicity k determined by whether the graph crosses (odd) or touches (even).
3. For a hole at x = c, include the common factor (x − c) in both numerator and denominator and cancel it; the graph will show a removable point at that x.
4. Use the horizontal/slant asymptote to set the degrees and leading coefficients:
- If horizontal asymptote y = 0, degree numerator < degree denominator.
- If y = L ≠ 0, degrees equal; leading coefficients’ ratio = L.
- If slant, degree numerator = degree denominator + 1 and perform polynomial long division.
5. Multiply by a constant A to match a known point (e.g., f(0) or any labeled point).

If you paste the graph or list the features, I’ll build the exact equation. If you have multiple-choice options, paste them and I’ll pick the correct one.