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

Determine the set of values that the function can possibly have.

Just in case, here is the graphed function:

graph{-x^2 [-5, 5, 10, 10]}

I hope this is helpful.

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To find the domain of ( f(x) = -x^2 ), it includes all real numbers since there are no restrictions on the input ( x ).

For the range, since ( f(x) = -x^2 ) represents a downward-opening parabola, the highest point is at the vertex. Since the coefficient of ( x^2 ) is negative, the maximum value occurs at the vertex. Therefore, the range is all real numbers less than or equal to the value of the vertex, which is ( -\infty ).

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The domain of ( f(x) = -x^2 ) is all real numbers (( \mathbb{R} )) because there are no restrictions on the values that ( x ) can take.

The range of ( f(x) = -x^2 ) is all real numbers less than or equal to 0, denoted as ( { y \in \mathbb{R} : y \leq 0 } ). This is because the function ( -x^2 ) will always yield non-positive values, with the maximum value being 0.

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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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