How do you find the domain and range of #f(x)=1/2(x2)#?
When graphing the function, we can quickly observe that: graph{0.5(x2) [10, 10, 5, 5]}
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To find the domain of ( f(x) = \frac{1}{2}(x2) ), we need to consider all possible values of ( x ) that make the function defined. Since ( x ) can take any real number value, the domain of ( f(x) ) is ( (\infty, \infty) ).
To find the range of ( f(x) = \frac{1}{2}(x2) ), we consider the possible output values of the function. As ( x ) varies across all real numbers, the function will produce all real numbers as output. Therefore, the range of ( f(x) ) is also ( (\infty, \infty) ).
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To find the domain and range of the function (f(x) = \frac{1}{2}(x  2)), we'll analyze the behavior of the function.

Domain: The domain of a function is the set of all possible input values (values of (x)) for which the function is defined. In this case, since the function is a rational function, the denominator cannot be zero. So, we set the denominator (x  2) not equal to zero and solve for (x): [x  2 \neq 0] [x \neq 2] Therefore, the domain of the function is all real numbers except (x = 2), or expressed in interval notation: ((∞, 2) \cup (2, +∞)).

Range: The range of a function is the set of all possible output values (values of (f(x))) that the function can produce. In this case, the function (f(x) = \frac{1}{2}(x  2)) is a linear function with a slope of (\frac{1}{2}) and a yintercept of (1) (when (x = 0)). Since it's a linear function, its graph is a straight line. The slope indicates that as (x) increases by 1, (f(x)) increases by (\frac{1}{2}). Since the domain is all real numbers except (x = 2), the range is also all real numbers except the value of (f(x)) when (x = 2). We can find the value of (f(x)) when (x = 2): [f(2) = \frac{1}{2}(2  2) = 0] So, when (x = 2), (f(x) = 0). This means that the range includes all real numbers except (0), or expressed in interval notation: ((∞, 0) \cup (0, +∞)).
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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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