general mathematics grade 11

1. Rational Functions, Equations, and
Inequalities
Senior High School | General
Mathematics

2. Learning Objectives
• - Differentiate rational functions, equations, and
inequalities
• - Solve rational equations and inequalities
• - Graph rational functions and identify domain,
intercepts, and asymptotes
• - Represent real-life situations using rational
functions

3. Introduction
• Ask: What happens to your speed if travel
time increases for the same distance?
• Answer: Speed decreases → This shows
inverse variation, a type of rational function.

4. Distinguishing Rational
Function, Rational Equation,
and Rational Inequality

5. Rational functions
A rational expression is a ratio of two
polynomials.

7. Key Characteristics
Rational Function: involves an input-output
relationship (e.g., domain, range, graph).
Rational Equation: asks, “What value(s) of x make
this equation true?”
Rational Inequality: asks, “What values of x make
this expression greater/less than another?”

8. Classify each expression as a rational function, rational
equation, or rational inequality:
RATIONAL FUNCTION
RATIONAL EQUATION
RATIONAL INEQUALITY
RATIONAL FUNCTION
RATIONAL INEQUALITY

9. Solving Rational Equations
Example 1: solve
Solutions

10. Solving Rational Equations
Example 2: solve
Solutions

11. Solving Rational Equations
Example 3: solve
Solutions

12. Solving Rational Equations
Example 4: solve
Solutions

13. Solving Rational Equations
Example 5: solve
Solutions

15. Solving Rational Inequality

16. Solving Rational Inequality

17. Solving Rational Inequality

18. Solving Rational Inequality

39. s

45. RATIONAL FUNCTIONS