Functions and Graphs Lecture (brief presentation)

A very brief presentation about functions and graphs.

1. Functions and Graphs Review of Functions • Basic Classes of Functions • Trigonometric Functions • Inverse Functions

2. Icebreaker: Is this a Function? Examples: - Teacher → Student ID - Teacher → Favorite Color - People → Birthday Ask students: Function or not?

3. What is a Function? • A function assigns each input to exactly one output • Function notation: f(x) • Example: f(x) = 2x + 3

4. Evaluating Functions Example: • f(x) = 2x + 3 • Find f(4) = ? Students solve and share answers.

5. Basic Classes of Functions • Linear – straight line • Quadratic – U-shaped parabola • Exponential – fast growth/decay • Rational – asymptotes Ask: Which is which?

6. Real-Life Applications • Savings over time → Linear • Ball thrown up → Quadratic • Population growth → Exponential • Speed vs. time → Varies

7. Trigonometric Functions • Sine, Cosine, Tangent • Derived from the unit circle • Graphs show periodic behavior • Example: Ferris wheel motion

8. Inverse Functions • Inverse undoes a function • Example: f(x) = 2x + 3 → f⁻¹(x) = (x-3)/2 • Graph: reflection across line y=x

9. Summary • Function definition • Types of functions • Trig functions • Inverse functions Quick review questions.