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sp2606 [1]
3 years ago
14

The end behaviour for the polynomial function h(x)=−x3+x4−2x+1 h ( x ) = - x 3 + x 4 - 2 x + 1 is: x→−[infinity], y→−[infinity]

x → - [infinity] , y → - [infinity] and x→[infinity], y→[infinity] x → [infinity] , y → [infinity] x→−[infinity], y→[infinity] x → - [infinity] , y → [infinity] and x→[infinity], y→[infinity] x → [infinity] , y → [infinity] x→−[infinity], y→−[infinity] x → - [infinity] , y → - [infinity] and x→[infinity], y→−[infinity] x → [infinity] , y → - [infinity] Unable to tell.
Mathematics
1 answer:
Goryan [66]3 years ago
6 0

Answer:

\text{As  } x \to \infty, y  \to \infty,$and as  x \to -\infty, y  \to \infty

Step-by-step explanation:

Given the polynomial function: h(x)=-x^3+x^4-2x+1

To examine its end behavior, we create a table of values that we can then examine.

\left|\begin{array}{c|c}x&h(x)\\--&--\\-4&329\\-3&115\\-2&29\\-1&5\\0&1\\1&-1\\2&5\\3&49\\4&185\end{array}\right|

From the table, we see a repeating pattern of positive values of h(x) with h(1)=-1 being an axis of symmetry.

Therefore, as:

x \to \infty, h(x)  \to \infty\\x \to -\infty, h(x)  \to \infty

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