Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Looking for a rational functions quiz algebra 2? Then this Algebra 2 quiz on Rational Functions: Asymptotes, Holes, and Graphs asks 10 multiple-choice questions with instant feedback.
Ten multiple-choice questions on rational functions: asymptotes, holes, domain, and inverse variation. Cancel common factors first, and keep track of which numbers belong to the vertical and horizontal asymptotes.
Standards: F-IF.C.7d, F-IF.B.4 · Level: Grade 11 Algebra 2
What this Rational Functions: Asymptotes, Holes, and Graphs quiz checks
- The domain excludes every zero of the denominator.
- A canceled factor creates a hole; a remaining denominator factor creates a vertical asymptote.
- The horizontal asymptote depends on the degrees: smaller top gives y = 0, equal degrees give the ratio of leading coefficients.
- y = a/(x − h) + k has asymptotes x = h and y = k.
- Inverse variation means xy = k, so the graph is y = k/x.
The 10 questions of the quiz
- Where is the vertical asymptote of y = 6x + 7 − 2?
- What is the horizontal asymptote of f(x) = 2x + 1x − 3?
- What does the graph of f(x) = x2 − 16x − 4 have at x = 4?
- The quantity y varies inversely with x, and y = 24 when x = 4. What is y when x = 8?
- Which equation matches the graph?
- Which values are excluded from the domain of f(x) = x − 5x2 − 81?
- As x grows very large, what happens to y = 8x?
- The graph shows f(x) = x2 − 6x + 8x − 2. What is the hole?
- Which describes y = –3x + 4 + 6 compared with y = 1x?
- What is the x-intercept of y = x − 1x + 3?
After the quiz
Missed a question? Reread the Rational Functions: Asymptotes, Holes, and Graphs lesson, then take the quiz again. Next, solve the Algebra 2 worksheet on Rational Functions: Asymptotes, Holes, and Graphs, one star first, then two and three stars. Finally, take the chapter test under real conditions, without notes and with a timer.
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