How do you find the domain and range of #y = -2x^2 - 8 #?

Answer 1

domain#->x in(-oo,+oo)#
range # ->y in (-oo,+oo)#

In the alphabet #color(red)(d)# comes before #color(red)(r)#
So #color(red)(d)#omain comes before #color(red)(r)#ange

Prior to output is input.

So domain#->#input#"; "#range#-># output
domain#->x in(-oo,+oo)# range # ->y in (-oo,+oo)#
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Answer 2

Domain: #x in(-infty,infty)#
Range: #y in [-8,-infty)#

The domain includes all the values of #x# that you can "legally" plug into the equation. If plugging in zero forced you to divide by zero or put a negative into a square root, those would be outside the domain of acceptable #x# values.
In the equation #y=-2x^2-8#, you are neither dividing by an #x# term, nor are you dealing with #x# values under a radical sign. Therefore, the domain includes all real numbers. That means you can plug in any real number you like, from #-infty# to #+infty#.
Domain: All real numbers, #RR#, which can be written as:
#x in(-infty,infty)#
The range is all the values of #y# that this function can produce. Because the equation is a quadratic equation, we have a parabola. That means that the maximum of the parabola is the upper bound of the equation and there is no lower bound.

The topmost portion of this function will be called the vertex.

Vertex: #x=-b/(2a)=-(0)/(2(-2))=0/4=0#
Plugging #0# into the function gives #y=-8#. So the range is
Range: All values of #y# less than #-8#, or
#y in [-8,-infty)#
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Answer 3

To find the domain and range of the function ( y = -2x^2 - 8 ):

  1. Domain: The domain of a quadratic function is all real numbers unless there are restrictions due to square roots or denominators. Since there are no square roots or denominators in this function, the domain is all real numbers. In interval notation, the domain is ( (-\infty, \infty) ).

  2. Range: The range of a quadratic function depends on the sign of the coefficient of the squared term. In this case, the coefficient is negative (-2), which means the parabola opens downwards. Therefore, the range will be all real numbers less than or equal to the maximum value of the function. Since there is no value added to or subtracted from the function, the maximum value occurs when ( x = 0 ).

    To find the maximum value, we can use the vertex form of the quadratic function: ( y = a(x - h)^2 + k ), where ( (h, k) ) is the vertex of the parabola. For the given function ( y = -2x^2 - 8 ), the vertex occurs at ( (0, -8) ). Since the parabola opens downwards, the range is all real numbers less than or equal to the y-coordinate of the vertex.

    Therefore, the range in interval notation is ( (-\infty, -8] ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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