What is the end behavior of #f(x) = 3x^(-2) + 4#?
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The end behavior of the function ( f(x) = 3x^{-2} + 4 ) can be determined by analyzing the behavior of the function as ( x ) approaches positive infinity and negative infinity.
As ( x ) approaches positive infinity (( x \rightarrow \infty )), the term ( x^{-2} ) becomes very small since ( x^{-2} ) is the reciprocal of ( x^2 ), which grows larger as ( x ) becomes larger. Therefore, the function behaves like ( 3(0) + 4 ) as ( x ) approaches positive infinity, which simplifies to ( 4 ). This means that the function approaches a horizontal asymptote at ( y = 4 ) as ( x ) goes to infinity.
Similarly, as ( x ) approaches negative infinity (( x \rightarrow -\infty )), the term ( x^{-2} ) becomes very small but positive. So, the function still behaves like ( 3(0) + 4 ) as ( x ) approaches negative infinity, which again simplifies to ( 4 ). Therefore, the function approaches the same horizontal asymptote ( y = 4 ) as ( x ) goes to negative infinity.
In summary, the end behavior of the function ( f(x) = 3x^{-2} + 4 ) is that it approaches the horizontal line ( y = 4 ) as ( x ) goes to positive infinity and negative infinity.
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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.
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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