1. Warm Up Find a triple if r = 10 and s = 2.
If a = 6, b = 8 and the triangle is a right triangle, what is the value of c?
If c = 50 and b = 48, what is the
value of a if it is a right
triangle?
1. a = 40, b= 96, c = 104
2. 10
3. 14 1 3 2

2. Lesson 4 Functions and Function Notation
Objective: To learn about functions, domains and ranges. To use function notation to represent functions

3. Functions
y = 3x + 1
For this equation, every x we choose, will give us a new y.
x is the input, and y is the output.
For every x we choose there is one and only one y possible – therefore this is a FUNCTION

4. Definition of a Function
A function is a correspondence between two sets X and Y that assigns to each element x of set X exactly one element y of set Y

5. Domain and Range
For each element x in X, the corresponding element y in Y is called the image of the function at x. The set X is called the domain of the function, and the set of all function values, Y is called the range of the function.

6. Ex 1: Determine whether each relation is a function.

7. Solution for part (a) 4 6 8 5 7 8

8. Solution for part (b) 4 5 6 6 7

9. Vertical Line Test (Pencil Test)
Given a graph – any vertical line drawn on the graph should only go through one point.
Function
Not a Function

10. Function Notation

11. Function Notation
The special notation f(x), read “f of x”, represents the value of the function at the number x.
The notation does not mean “ f times x.”

12. Finding a Function’s Domain
The domain (the x’s) of a function can be almost any real number. There are two cases when there are exceptions:
Division by zero – if x is in the bottom of the fraction (denominator), then x cannot make that denominator 0.
f(x) = ; x = 3 is not defined.

13. Finding a Function’s Domain
Even roots of negative numbers
y = is only a real number if x ≥ 1

14. Finding a Function’s Domain

15. Ex 5: Find the domain of each function

16. Solution part a

17. Solution part b

18. Solution part c

19. Practice Exercises

20. Answers

21. Graphing Functions Using a graphing calculator
Put the equation or function into the form y = ….
Button at top left y =
Then type in the rest of the equation and press [GRAPH] at top right.

22. Evaluating Functions Given f(x) = x2 + 2x – 1, find f(2).
This means to plug in 2 wherever there is an x in the function.
f(2) = (2)2 +2(2) – 1        = – 1        = 7

23. Evaluating Functions Given f(x) = x2 + 2x – 1, find f(–3).

24. Practice f(x) = x2 + 3x- 4, find f(-2) & f(0)
f(x) = x2 + 1, find f(-3) & f(x-1)
-6, -4
10, x^2 – 2x +2

25. Practice
Find the numbers for x whose image is 2.
f(x) = x2
x =√2