Domain:
x ∈ R or x ∣ ( − ∞ ,
Range : y ≥ 1 or y ∣ [ 1 , ∞ ) .
Step-by-step explanation:
y
=
x
2
+
1
, Domain : Possible input value of
x
is
any real value . Therefore Domain:
x
∈
R
or
x
∣
(
−
∞
,
∞
)
.
Range:
y
=
x
2
+
1
or
y
=
(
x
−
0
)
2
+
1
. Comparing with vertex
form of equation
f
(
x
)
=
a
(
x
−
h
)
2
+
k
;
(
h
,
k
)
being vertex
we find here
h
=
0
,
k
=
1
,
a
=
1
∴
Vertex is at
(
0
,
1
)
Since
a
is positive the parabola opens upward and
vertex is the minimum point
x
=
0
,
y
=
1
So range is
y
≥
1
or
y
∣
[
1
,
∞
)
.
Domain:
x
∈
R
or
x
∣
(
−
∞
,
∞
)
Range :
y
≥
1
or
y
∣
[
1
,
∞
)
.
graph{x^2+1 [-10, 10, -5, 5]}
