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Llana [10]
3 years ago
14

15 Points! Find the range of the functions: f(x) = (x + 1)^2 - 1 f(x) = 7x - 11

Mathematics
1 answer:
MakcuM [25]3 years ago
4 0

In both cases you may well benefit from graphing the functions.

Do you recognize f(x) = (x + 1)^2 - 1 as a quadratic function, whose graph is that of a parabola that opens up? By comparing this to y = a(x-h)^2 + k, we see that a=1, h= -1 and k = -1. The vertex is at (h,k), which here is the point (-1, -1). This is the minimum value of the function. Thus, the range of this function is [-1, infinity).


Now for the function f(x) = 7x - 11: This is a linear function whose graph is (surprise!) a straight line. When x increases, y increases, without limits to either. Similarly, when x decreases, y decreases.

Thus the range includes all real numbers: (-infinity, infinity).

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A manufacturing company plans to progressively increase its production capacity over the next few quarters. (A quarter is a peri
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Answer:

  5 months

Step-by-step explanation:

We assume that y represents production capacity, rather than <em>increase</em> in production capacity. Then we want to solve the 6th-degree equation ...

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This can be factored in groups as ...

  x^4(x^2 -25) + 199(x^2 -25) = 0

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This has 4 complex solutions and 2 real solutions.

  x^2 = 25

  x = ±5

The duration required for capacity to reach 4975 units is 5 months.

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Find the area and thank
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40 meters

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6 0
2 years ago
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The coordinate plane below shows the location of f, a linear function. Function g is described by the equation g (x) = 1.5 + 3.
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Which rule describes the composition of transformations that maps pre- image ABCD to final image A“B“C“D“?
Svetlanka [38]

Answer:

1. Reflection across the x-axis

2. Translation 6 units to the left and 1 unit up

Step-by-step explanation:

The quadrilateral ABCD has its vertices at points A(3,5), B(6,5), C(4,1) and D(1,1).

1. Reflect quadrilateral ABCD across the x-axis. This reflection has the rule:

(x,y)\rightarrow (x,-y),

then

A(3,5)\rightarrow A'(3,-5)\\ \\B(6,5)\rightarrow B'(63,-5)\\ \\C(4,1)\rightarrow C'(4,-1)\\ \\D(1,1)\rightarrow D'(1,-1)

2. Translate quadrilateral ABCD 6 units to the left and 1 unit up. This translation has the rule:

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then

A'(3,-5)\rightarrow A''(-3,-4)\\ \\B'(6,-5)\rightarrow B''(0,-4)\\ \\C'(4,-1)\rightarrow C''(-2,0)\\ \\D'(1,-1)\rightarrow D''(-5,0)

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