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pashok25 [27]
3 years ago
10

state the domain, the range, and the intervals on which function is increasing, decreasing, or constant in interval notation

Mathematics
1 answer:
erma4kov [3.2K]3 years ago
8 0

Answer:

  • domain (-∞, ∞)
  • range (-∞, 4]
  • increasing (-∞, 0)
  • decreasing (0, ∞)
  • constant (only at x=0, not on any interval)

Step-by-step explanation:

The graph is of the equation y = -x^2 +4. It is a polynomial of even degree, so has a domain of all real numbers: (-∞, ∞).

The vertical extent of the graph includes y=4 and all numbers less than that:

  range: (-∞, 4]

The graph is increasing to the left of its vertex at x=0, decreasing to the right.

  increasing (-∞, 0); decreasing (0, ∞)

There is no interval on which the function is constant. It has a horizontal tangent at x=0, but a single point does not constitute an interval.

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3 years ago
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Identify the center and radius for the circle with the following equation; (x+5)^2+y^2+12y=3
rosijanka [135]
Center: (-5,-6)
Radius: 39
How to do it

Complete the square for
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(
y
+
6
)
2
−
36
(
y
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2
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(
y
+
6
)
2
−
36
(
y
+
6
)
2
-
36
for
y
2
+
12
y
y
2
+
12
y
in the equation
(
x
+
5
)
2
+
y
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12
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=
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(
x
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5
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2
+
y
2
+
12
y
=
3
.
(
x
+
5
)
2
+
(
y
+
6
)
2
−
36
=
3
(
x
+
5
)
2
+
(
y
+
6
)
2
-
36
=
3
Move
−
36
-
36
to the right side of the equation by adding
36
36
to both sides.
(
x
+
5
)
2
+
(
y
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6
)
2
=
3
+
36
(
x
+
5
)
2
+
(
y
+
6
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2
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3
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36
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(
x
+
5
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2
+
(
y
+
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)
2
=
39
(
x
+
5
)
2
+
(
y
+
6
)
2
=
39
This is the form of a circle. Use this form to determine the center and radius of the circle.
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5 0
3 years ago
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