F(x) =(x+1)-2 domain and ran
Answers
Answer:
The domain is all real numbers
R
or in interval notation
(
−
∞
,
∞
)
.
The range is
y
≥
2
or in interval notation
[
2
,
∞
)
.
Explanation:
f
(
x
)
=
(
x
−
1
)
2
+
2
=
1
(
x
−
1
)
2
+
2
The easiest way to find the domain and range of a quadratic function is to look at the graph.
The general equation of a parabola in vertex form is
y
=
a
(
x
−
h
)
2
+
k
where
(
h
,
k
)
is the vertex.
A positive
a
means the parabola is upward facing (U shaped) and a negative
a
means it is downward facing (an upside down U shape).
The vertex of this example is then
(
1
,
2
)
.
a
=
+
1
so the shape is an upward facing parabola.
The domain is found by considering all the possible values of
x
.
Looking at the graph, you can see that
x
goes all the way from negative infinity to positive infinity. The domain can be expressed as all real numbers
R
, or in interval notation,
(
−
∞
,
∞
)
.
The range is found by considering all the possible values of
y
.
There are no values of
y
below
y
=
2
, so
y
≥
2
. In interval notation, the range is
[
2
,
∞
)
.
graph{(x-1)^2+2 [-10.12, 9.88, -2.4, 7.6]}