Question

2.

(01.02 MC)

A polynomial function g(x) has a positive leading coefficient. Certain values of g(x) are given in the following table.

x –4 –1 0 1 5 8 12
g(x) 0 3 1 2 0 –3 0


If every x-intercept of g(x) is shown in the table and each has a multiplicity of one, what is the end behavior of g(x)? (5 points)
As x→–∞, g(x)→–∞ and as x→∞, g(x)→–∞.
As x→–∞, g(x)→ –∞ and as x→∞, g(x)→∞.
As x→–∞, g(x)→∞ and as x→∞, g(x)→–∞.
As x→–∞, g(x)→∞ and as x→∞, g(x)→∞.

Answer 1

As x→–∞, g(x)→–∞ and as x→∞, g(x)→–∞. This is because the leading coefficient of g(x) is positive, which means that the graph of g(x) will always increase as x increases, and it will always decrease as x decreases. Therefore, the graph of g(x) will have a negative end behavior.

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