Rational Function
A function written as one polynomial divided by another polynomial.
Back to NC Math 3 Home6 Practice Sets Complete
Math 3 Strand
Rational Functions
This strand review helps students connect rational expressions, graphs, and calculator-based checks so they can recognize restrictions and graph behavior faster on the NC Math 3 EOC.
Focus on domain restrictions, holes, vertical and horizontal asymptotes, intercepts, and solving rational equations while using Desmos strategically to compare tables, equations, and graph behavior.
Confidence Check
If you can move through Sets 1 to 6 in order, explain why a value creates a hole or an asymptote, and use Desmos to test solutions and graph behavior, you are building real NC Math 3 EOC readiness.
Objectives Covered
- Identify domain restrictions quickly so excluded x-values do not become EOC mistakes.
- Connect simplified rational expressions to holes, vertical asymptotes, and intercepts.
- Interpret how numerator and denominator behavior affects graph shape and end behavior.
- Solve rational equations carefully and check for extraneous solutions caused by restrictions.
- Use Desmos to compare tables, graphs, and symbolic work when analyzing asymptotes and holes.
- Model real-world situations with rational functions and explain what restrictions mean in context.
Key Vocabulary
Student-Friendly Terms to Know
These words appear often in class, in Desmos work, and on rational-function EOC questions.
Domain Restriction
A value of x that is not allowed because it makes the denominator equal 0.
Vertical Asymptote
A vertical line the graph approaches when the denominator is 0 and the factor does not cancel.
Horizontal Asymptote
A horizontal line that shows the y-value the graph approaches far to the left or right.
Hole
A missing point on the graph caused by a factor that cancels from the numerator and denominator.
Intercept
A point where the graph crosses the x-axis or y-axis.
Extraneous Solution
A value that appears while solving an equation but is not actually allowed in the original problem.
Simplify
To rewrite an expression in a cleaner form while keeping its original restrictions.
Practice Questions
Choose a Rational Functions Practice Set
All 6 sets are ready to use. Start with the direct skill-builders, then move into mixed review and challenge work to build steadier EOC confidence.
Recommended Practice Order
Sets 1 to 6 for Most Students
This order moves from core rational skills to mixed review so students can build confidence before the final readiness check.
1
Practice Set 1
Start with graph and expression basics.
Review restrictions, intercepts, holes, and asymptotes before moving to multi-step work.
2
Practice Set 2
Connect equations to graphs.
Match simplified forms, graph behavior, and solutions of rational equations.
3
Practice Set 3
Push into stronger reasoning.
Explain why restrictions matter and justify graph or algebra choices in richer tasks.
4
Practice Set 4
Practice switching question types.
Move between quick skill checks, graph analysis, and solving equations with care.
5
Practice Set 5
Take on EOC-style challenge items.
Blend graph behavior, algebraic reasoning, and application questions in one set.
6
Practice Set 6
Finish with a readiness check.
Use a final mixed set to test pacing, accuracy, and confidence before broader review.
Practice Set 1
DOK 1 Practice Set
Review domain restrictions, asymptotes, holes, intercepts, and simplifying rational expressions.
Practice Set 2
DOK 2 Practice Set
Connect equations, tables, and graphs while solving rational equations and interpreting graph behavior.
Practice Set 3
DOK 3 Practice Set
Use strategic reasoning to justify restrictions, compare representations, and analyze rational models.
Practice Set 4
Mixed Practice A
Blend graph features, simplifying, and solving work so students practice switching demands smoothly.
Practice Set 5
EOC Challenge Set
Tackle stronger rational function questions with asymptote reasoning, extraneous solutions, and real-world interpretation.
Practice Set 6
Mixed Readiness Check
Finish with a short rational review set that checks accuracy, pacing, and overall EOC readiness.