How do you describe the end behavior of #f(x)=2x^2+12x+12#?

Answer 1

Elias Ackerman

#x rarr ∞, y rarr ∞# and as #x rarr -∞, y rarr ∞#

Graph #f(x)# so you can see the shape of it.

graph{2x^2+12x+12 [-12.58, 7.42, -7.4, 2.6]}

We can see that as #x rarr ∞, y rarr ∞# and as #x rarr -∞, y rarr ∞#

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Answer 2

Sadie Ackerman

To describe the end behavior of ( f(x) = 2x^2 + 12x + 12 ):

As ( x ) approaches positive infinity (( +\infty )), ( f(x) ) increases without bound. As ( x ) approaches negative infinity (( -\infty )), ( f(x) ) also increases without bound.

This behavior indicates that the leading term, ( 2x^2 ), dominates the function's behavior as ( x ) becomes very large or very small.

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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.