![2.1 Functions Obj: Define a function
Practice:
a) Domain: R – {0, 1}
b) Domain: [-3, 3]
c) Domain: (-1, oo)](https://image.slidesharecdn.com/2-241212164946-e2301219/85/2-1-Functions-PPT-1-FOR-STUDRNT-MUST-REA-20-320.jpg)
2.1 Functions PPT 1 FOR STUDRNT MUST REA
- 1. 2.1 Functions Obj: Define a function
- 2. 2.1 Functions • A relation is considered a Function if there is exactly one output for each input Obj: Define a function
- 3. 2.1 Functions Obj: Define a function The temperature of water from the faucet is a function of time.
- 4. 2.1 Functions Obj: Define a function INPUT (DOMAIN) OUTPUT (RANGE) FUNCTION MACHINE For a relationship to be a function… EVERY INPUT MUST HAVE AN OUTPUT TWO DIFFERENT INPUTS CAN HAVE THE SAME OUTPUT Functions ONE INPUT CAN HAVE ONLY ONE OUTPUT
- 5. 2.1 Functions Obj: Define a function Example No two ordered pairs can have the same first coordinate (and different second coordinates). Which of the following relations are functions? R= {(9,10), (-5, -2), (2, -1), (3, -9)} S= {(6, a), (8, f), (6, b), (-2, p)} T= {(z, 7), (y, -5), (r, 7), (z, 0), (k, 0)}
- 6. 2.1 Functions Obj: Define a function
- 7. 2.1 Functions Obj: Define a function
- 8. 2.1 Functions Obj: Define a function
- 9. 2.1 Functions Obj: Define a function
- 10. 2.1 Functions Obj: Define a function a) Express how “f” acts on the input “x” to produce f(x) b) Evaluate f(3), f(-2), and f() c) Find the domain and range of “f” a) X F(x) -2 8 -1 5 0 4 1 5 b) f(3) = 3^2 + 4 = 13 F(-2) = 4 + 4 = 8 F() = 5 + 4 = 9 c) Domain: All real numbers Range: [4, oo)
- 11. 2.1 Functions Obj: Define a function
- 12. 2.1 Functions Obj: Define a function
- 13. 2.1 Functions Obj: Define a function Ex2: f(x) = 2x2 – 3 Find f(0), f(-3), f(5).
- 14. 2.1 Functions Obj: Define a function Ex3:
- 15. 2.1 Functions Obj: Define a function
- 16. 2.1 Functions Obj: Define a function
- 17. 2.1 Functions Obj: Define a function 1) f(x) = x2 + 2 2) g(x) = √x – 1 3) h(x) = 1 x + 5 Practice: Find the domain and range for the following:
- 18. 2.1 Functions Obj: Define a function 1) f(x) = x2 + 2 2) g(x) = √x – 1 2) h(x) = 1 x + 5 Practice: Find the domain and range for the following: Domain: R Range: [2, oo) Domain: [0, oo) Range: [-1, oo) Domain: R {-5} Range: (-oo, -5) U (- 5, oo)
- 19. 2.1 Functions Obj: Define a function Practice:
- 20. 2.1 Functions Obj: Define a function Practice: a) Domain: R – {0, 1} b) Domain: [-3, 3] c) Domain: (-1, oo)
- 21. 2.1 Functions Obj: Define a function Authentic example, Real life:
- 22. 2.1 Functions Obj: Define a function Authentic example, Real life:
- 23. 2.1 Functions Obj: Define a function Piecewise Defined Function:
- 24. 2.1 Functions Obj: Define a function Piecewise Defined Function:
- 25. 2.1 Functions Obj: Define a function Piecewise Defined Function: ‘Piecewise Function’ What Are They? Up to now, we’ve been looking at functions represented by a single equation. In real life, however, functions are represented by a combination of equations, each corresponding to a part of the domain. These are called piecewise functions. Piecewise Function –a function defined by two or more functions over different parts, or pieces, of the domain.
- 26. 2.1 Functions Obj: Define a function 1 , 1 3 1 , 1 2 x if x x if x x f One equation gives the value of f(x) when x ≤ 1 and the other when x>1
- 27. 2.1 Functions Obj: Define a function 2 , 1 2 2 , 2 ) ( x if x x if x x f First you have to figure out which equation to use, you NEVER use both X=0 This one fits Into the top equation So: 0+2=2 f(0)=2 X=2 This one fits here So: 2(2) + 1 = 5 f(2) = 5 X=4 This one fits here So: 2(4) + 1 = 9 f(4) = 9
- 28. 2.1 Functions Obj: Define a function Evaluating Piecewise Functions Evaluating piecewise functions is like evaluating functions that you are already familiar with. f(x) = x2 + 1 , x 0 x – 1 , x 0 Let’s calculate f(2). You are being asked to find y when x = 2. Since 2 is 0, you will only substitute into the second part of the function. f(2) = 2 – 1 = 1