# How do you find the domain and range of #f(x) = x^3 - 3x + 2#?

Domain simply asks, "Where does the function exist on the x-axis?" So, in this function, because

Similarly, range asks, "Where does the function exist on the y-axis?" When you plug the function into a graph, it becomes evident that it will forever go upward toward infinity and forever downwards toward negative infinity on both axes.

This image shows the basic graph of

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To find the domain of ( f(x) = x^3 - 3x + 2 ), we need to determine all possible values of ( x ) for which the function is defined. Since ( f(x) ) is a polynomial function, it is defined for all real numbers. Therefore, the domain of ( f(x) ) is ( \mathbb{R} ), the set of all real numbers.

To find the range of ( f(x) = x^3 - 3x + 2 ), we can analyze the behavior of the function as ( x ) approaches positive and negative infinity. As ( x ) approaches positive infinity, ( x^3 ) dominates the expression, leading to a positive value. Similarly, as ( x ) approaches negative infinity, ( x^3 ) dominates the expression, leading to a negative value. Therefore, the range of ( f(x) ) is ( \mathbb{R} ), the set of all real numbers.

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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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