Precalculus Examples

Find the Domain and Range f(x)=sin(x)
f(x)=sin(x)f(x)=sin(x)
Step 1
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation:
(-,)(,)
Set-Builder Notation:
{x|x}
Step 2
The range is the set of all valid y values. Use the graph to find the range.
Interval Notation:
[-1,1]
Set-Builder Notation:
{y|-1y1}
Step 3
Determine the domain and range.
Domain: (-,),{x|x}
Range: [-1,1],{y|-1y1}
Step 4
image of graph
(
(
)
)
|
|
[
[
]
]
7
7
8
8
9
9
°
°
θ
θ
4
4
5
5
6
6
/
/
^
^
×
×
>
>
π
π
1
1
2
2
3
3
-
-
+
+
÷
÷
<
<
,
,
0
0
.
.
%
%
=
=
 [x2  12  π  xdx ]