How do you find the end behavior of #f(x) = - 6x^2 + 14x + 21#?
It would fall to the left and fall to the right
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To find the end behavior of the function ( f(x) = -6x^2 + 14x + 21 ):
- Examine the leading term: ( -6x^2 ).
- As ( x ) approaches positive infinity, the term ( -6x^2 ) dominates, and since ( x^2 ) grows much faster than ( x ), ( f(x) ) approaches negative infinity.
- As ( x ) approaches negative infinity, the term ( -6x^2 ) still dominates, and since ( x^2 ) grows much faster than ( x ), ( f(x) ) also approaches negative infinity.
Therefore, the end behavior of ( f(x) = -6x^2 + 14x + 21 ) is as follows:
- As ( x ) approaches positive infinity, ( f(x) ) approaches negative infinity.
- As ( x ) approaches negative infinity, ( f(x) ) also approaches negative infinity.
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To find the end behavior of the function f(x) = -6x^2 + 14x + 21, we look at the leading term of the polynomial, which is -6x^2. The leading coefficient is -6, and the degree of the polynomial is 2.
Since the leading coefficient is negative and the degree of the polynomial is even, the end behavior of the function is as follows:
- As x approaches negative infinity, the value of f(x) approaches negative infinity.
- As x approaches positive infinity, the value of f(x) approaches negative infinity.
Therefore, the end behavior of the function f(x) = -6x^2 + 14x + 21 is that it decreases without bound as x approaches negative or positive 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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