How do you find the domain and range of #y = 2x^2  8 #?
domain
range
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Domain:
Range:
The topmost portion of this function will be called the vertex.
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To find the domain and range of the function ( y = 2x^2  8 ):

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) ).

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 ycoordinate of the vertex.
Therefore, the range in interval notation is ( (\infty, 8] ).
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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