Grade 11 · Algebra & Functions
Rational Functions
Learn to connect inputs and outputs and analyze how quantities change through clear explanations, worked examples, an interactive model, and guided practice.
Lesson coverage
Learn the whole topic, not just one problem type.
This lesson and its practice bank deliberately rotate across these core facets so students build a connected understanding of the subject.
Evaluate functions for given inputs.
Connect equations, tables, graphs, and verbal rules.
Interpret slope or another changing relationship.
Compare behavior across representations.
Use functions to represent real relationships.
Build the idea
Rational Functions is part of the extend functions and algebra to polynomial, rational, radical, exponential, logarithmic, complex, and trigonometric relationships. Start by identifying what each quantity, symbol, diagram, or graph represents before calculating.
Inputs & outputs
Evaluate functions for given inputs. Use a representation that fits the idea, connect it to the relevant mathematical relationship, and explain how the representation supports the result.
Representations
Connect equations, tables, graphs, and verbal rules. Use a representation that fits the idea, connect it to the relevant mathematical relationship, and explain how the representation supports the result.
Rate of change
Interpret slope or another changing relationship. Use a representation that fits the idea, connect it to the relevant mathematical relationship, and explain how the representation supports the result.
Compare functions
Compare behavior across representations. Use a representation that fits the idea, connect it to the relevant mathematical relationship, and explain how the representation supports the result.
Modeling
Use functions to represent real relationships. Use a representation that fits the idea, connect it to the relevant mathematical relationship, and explain how the representation supports the result.
Use a reliable strategy
Translate the information into symbols, apply one valid transformation at a time, and check the result in the original relationship.
Check and explain
A correct answer is only part of mathematical understanding. Check units, signs, scale, and whether the result makes sense. Then explain the relationship in words so you can recognize the same structure when the numbers or context change.
Key terms
Words to know
- Rational Functions
- The central skill or relationship explored in this lesson.
- Function
- A rule assigning each input exactly one output.
- Input
- A value supplied to a function.
- Output
- The result produced by a function.
Interactive math lab
Change it. See it. Understand it.
Adjust the values and watch the relationship respond.
| Input | 6 |
|---|---|
| Offset | 3 |
| Output | 15 |
Worked examples
See the idea in action.
When x=3, y=7.
The coefficient of x is the slope/rate of change: 3.
Guided practice
20 questions drawn from a 150-question lesson bank.
Each practice session mixes the major skills in this lesson so you practice the whole topic, not just one repeated problem type.
If f(x)=1x+0, what is f(2)?
Curriculum reference
Built as a continuous K–12 progression.
The sequence follows widely used K–12 mathematics progressions and references the Common Core mathematics framework. Explanations, examples, interactive models, and practice questions are original FreeLearnHub material.