Download H. Algebra 2 2.1 Relations and Functions Relation: Set of input (x

H. Algebra 2
2.1 Relations and Functions
Relation: Set of input (x) values and output (y) values which can be written as an ordered pair
Domain: set of all inputs or x-coordinates of the ordered pairs
Range: set of all outputs or y-coordinates of the ordered pairs
Function: A relation in which each element of the domain is paired with EXACTLY one element in the range
D
D
R
D
R
R
-1
-2
-1
0
3
5
4
-1
-1
3
3
0
7
5
1
10
0
2
3
Vertical Line Test- Used to determine whether the relation has at least one element of the domain paired with
more than one element of the range. If the vertical line passes through two or more points on the graph
(same x value with 2 different y values), then the relation is not a function
a.
b.
Practice: pg. 59 # 1, 7, 8, 12, 17, 18, 20
Example of functions and how to read them:
a.
b.
Input
Function
c.
Output
Ordered Pair
Example of evaluating a function:
2. Given g(t) = 7t2 + 1
1. Given f(x) = x + 7
a.
f(5)
b. f(-2)
3. Given h(x) = -3x + 5
a. h(x)
c. f(x+2)
a. g(2) – g(-3)
b. g(0)
4. Given f(x) = | 3x |
b. h(x – 2)
a. Complete the ordered pair (-12, ?)
b. Complete the ordered pair (?, 15)
Application:
1. The area of a square is function of the length of a side of the square.
a. Write a function rule for the area of a square.
b. Evaluate the function for a square with a side length of 3.5 inches
2. The volume of a sphere is a function of the radius of the sphere.
a. Write a function for the volume of a ball.
b. Evaluate the function for the volume with a radius of 10.5cm
H. Algebra 2
Exit Quiz
Name: ____________________________________
Evaluate each function for the given values of x:
1.
f ( x) 
2.
1 2
x 8
2
a. f(2)
b. f(-1)
c. f(x) = 0; solve for x.
f ( x)  ( x  3) 2  4
a. f(-3)
b. f(0) + f(-1)
c. f(x) = 85; solve for x.
3.
g ( x)  4  3 x 2
a.
1
b. g  
2
c. g(x) = -8; solve for x.
4.
g ( x)  x  1
a. g(3)
b. g(-10)
c. g(x) = 3; solve for x.
g (2)
g (3)