Graphing Polynomial Functions — Quiz

Question 5 • Mathematics III

What is the end behavior of the graph of the polynomial function f of x is equal to 2 x cubed minus 26 x minus 24 ?

Answer

As x rightarrow negative infinity , y rightarrow infinity and as x rightarrow infinity , y rightarrow infinity .

As x rightarrow negative infinity , y rightarrow negative infinity and as x rightarrow infinity , y rightarrow infinity .

As x rightarrow negative infinity , y rightarrow infinity and as x rightarrow infinity , y rightarrow negative infinity .

As x rightarrow negative infinity , y rightarrow negative infinity and as x rightarrow infinity , y rightarrow negative infinity .

Explanation

The end behavior is determined by the leading term, 2x³, because it grows faster than the other terms. It has odd degree and a positive coefficient, so as x approaches negative infinity, f(x) approaches negative infinity; as x approaches positive infinity, f(x) approaches positive infinity. This matches choice D.

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