How do you find the domain and range of #y = 4x  x ^2#?
Domain:
Range:
plot{x(4x) [6.4, 6.087, 1.347, 4.897]}
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To find the domain and range of the function y = 4x  x^2, we need to analyze the behavior of the function.

Domain: The domain of a function is the set of all possible input values (xvalues) for which the function is defined. Since the function is a polynomial, there are no restrictions on the input values. Therefore, the domain is all real numbers, or (∞, ∞).

Range: The range of a function is the set of all possible output values (yvalues) that the function can produce. To find the range, we can analyze the behavior of the function. Since the function is a quadratic function with a negative coefficient for the x^2 term, it opens downward. Therefore, the maximum value of the function occurs at the vertex. The xcoordinate of the vertex of the quadratic function y = ax^2 + bx + c is given by x = b/(2a). In this case, a = 1 and b = 4. Plugging these values into the formula, we get x = 4/(2*(1)) = 2. To find the corresponding ycoordinate (maximum value), we plug x = 2 into the function: y = 4(2)  2^2 = 8  4 = 4. Therefore, the maximum value of the function is 4. Since the function is a quadratic function, it approaches negative infinity as x approaches positive or negative infinity. Thus, the range of the function is (∞, 4].
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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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