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What is the range of the function #f(x) = x^3 + 5#?

Answer 1

The range of the function is all real numbers, or #(-oo, oo)# (interval notation).

Range refers to where all the y-values can be in the graph.

The range of the function is all real numbers, or #(-oo, oo)# (interval notation).

Here is the graph of the function (there should be arrows at each end, just not shown in the graph) to prove why the range is all real numbers:

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Answer 2

Isaiah Anthony

To find the range of the function ( f(x) = x^3 + 5 ), we need to consider the behavior of the cubic function as ( x ) approaches positive and negative infinity. Since ( x^3 ) will become increasingly large as ( x ) moves away from zero in either direction, the range of the function will be all real numbers. Therefore, the range of the function ( f(x) = x^3 + 5 ) is ( (-\infty, \infty) ).

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Answer from HIX Tutor

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.