1. Warm Up
Given y = –x² – x + 2 and the x-value, find the y-value in each…
1. x = –3, y = ____
2. x = 0, y = ____
3. x = 1, y = ____ –4
– −3 2 – (–3) + 2 – 2
–6 + 2 –4
– – (0) + 2
– – (1) + 2
0 – 0 + 2
–1 – (1) + 2 2
–2 + 2

2. Functions

3. Relation:
- a set of ordered pairs
Domain:
- the set of all x-values
- also known as the set of inputs
Range:
- the set of all y-values
- also know as the set of outputs.
Function:
- relation where each x-value
has exactly one y-value

4. Testing for Functions function Not a function function function
Let A = { 2, 3, 4, 5, } and B = { -3, -2, -1, 0, 1 }. Which of the following sets of ordered pairs represents functions from set A to set B? a. { (2, -2), (3, 0), (4, 1), (5, -1) } b. { (4, -3), (2, 0), (5, -2), (3, 1), (2, -1) } c. { (2, -1), (3, -1), (4, -1), (5, -1) } d. { (3, -2), (5, 0), (2, -3) }
function
Not a function
function
function

5. - test used to determine if the graph
The Vertical Line Test
- test used to determine if the graph
is a function.
Examples:
f(x) = {-x +3, x ≤ 2}
x = y² y= x4 + x x x² + y² = {2x - 2, x ≥ 4}
Not a Function
Function
Not a Function
Function

6. Function Notation y = f(x) Example: f is the name of the function.
y is the dependent variable, or output value.
x is the independent variable, or input value.
f(x) is the value of the function of x.
Example:
IF… f(x) = 2x + 1 and you want to find f(3)
THEN… x = 3 and f(3) is the y value that
corresponds to that.
Read as “f of x”

7. f(x) = 4x² – 2x + 5, find f(3) f(x) = 𝑥 −1 𝑥 , find f(–2)
Examples
f(x) = 4x² – 2x + 5, find f(3)
f(x) = 𝑥 −1 𝑥 , find f(–2)
f(x) = |–3x + 8|, find f(4) 35
– 2(3) + 5
36 – 6 + 5
4(9) – 6 + 5
30 + 5
−2−1 −2
−3 −2
3 2
−3 4 +8
−12+8 −4 4

8. If f(x) = x² + 7, find each: 4. f(3a) 5. f(b – 1) (3𝑎) 2 + 7 9 𝑎 2 + 7
Examples
If f(x) = x² + 7, find each:
4. f(3a)
5. f(b – 1)
(3𝑎)
9 𝑎
(𝑏−1)
(b – 1)(b – 1) + 7
𝑏 2 – b – b + 8
𝑏 2 – 2b + 8

9. 6. 𝑓 𝑥+𝑦 −𝑓(𝑥) 𝑦 (𝑥+𝑦) 2 + 7−( 𝑥 2 +7) 𝑦 𝑥 2 +2𝑥𝑦+ 𝑦 2 + 7− 𝑥 2 −7 𝑦
6. 𝑓 𝑥+𝑦 −𝑓(𝑥) 𝑦
(𝑥+𝑦) 2 + 7−( 𝑥 2 +7) 𝑦
𝑥 2 +2𝑥𝑦+ 𝑦 2 + 7− 𝑥 2 −7 𝑦
2𝑥𝑦+ 𝑦 2 𝑦
𝑦(2𝑥+𝑦) 𝑦
2x + y

10. Classwork and Homework
Pgs
#’s 1-3, 8-14 even,
17-27 odd, 29, 31, 34, 36