2x+5=17
x=6
What circle should you use for x>4 (open or closed)
Open Circle
The complete set of all possible input values in a function.
Domain
f(x)=x+3 find f(2)
f(2)=5
Does this graph represent a function ?
Yes, this graph passes the vertical line test!
3x-7=2x+5
x=12
Solve and describe the number line for
2x+3<11
x<4 open circle at 4 shaded to the left
The relation or rule that assigns each input exactly one output.
Function
f(x)=2x-1 find f(5)
f(5)=9
Identify the domain 
-4<=x<=6
4(x-3)+2=18
x=7
Solve and describe the number line for
-2(4n-5)>=58
n<=-6
Where any vertical line drawn on the graph will pass through exactly one point.
Vertical Line Test.
f(x)=7(x-5)+3 find f(4)
f(4)=-4
Identify the Range
0<=y<=infinity
5(2x-3)-4=3x+12
x=5
Solve and describe the number line for
-6x-4<=2(x-10)
2<=x
This test can be used to know if a function is one-to-one
Horizontal Line Test
f(x)=2x+6 find f(x)=4
f(-1)=4
Is this function one-to-one ?
No, this graph fails the horizontal line test!
3(2x-5)+4=2(x+7)+5x
x=-4
Solve and describe the number line for
2(x+1)>3(2x-4)
x<7/2
We say this to describe the domain or range when any real value can be used.
All Real Numbers
f(x)=3(x-5)-7 find f(x)=20
f(14)=20
Is this a function? What is the domain and range?
No this is not a function. The domain is 0<=x<=infinity. The range is -infinity<=y<=infinity