Question

The leading term of f(x) is −7x.

Part A: What is the correct verbal description of the end behavior of f(x)?

Part B: What is the correct symbolic description of the end behavior of f(x)?

Select one answer for Part A, and one answer for Part B.

B: As x→∞, f(x)→−∞, and as x→−∞, f(x)→−∞.
A: As x approaches infinity, f(x) approaches negative infinity, and as x approaches negative infinity, f(x) approaches infinity.
B: As x→∞, f(x)→−∞, and as x→−∞, f(x)→∞.
A: As x approaches infinity, f(x) approaches negative infinity, and as x approaches negative infinity, f(x) approaches negative infinity.
A: As x approaches infinity, f(x) approaches infinity, and as x approaches negative infinity, f(x) approaches infinity.
B: As x→∞, f(x)→∞, and as x→−∞, f(x)→∞.
A: As x approaches infinity, f(x) approaches infinity, and as x approaches negative infinity, f(x) approaches negative infinity.
B: As x→∞, f(x)→∞, and as x→−∞, f(x)→−∞.

Answer 1

A: As x approaches infinity, f(x) approaches negative infinity, and as x approaches negative infinity, f(x) approaches infinity.

B: As x→∞, f(x)→−∞, and as x→−∞, f(x)→∞

Explanation:

The negative leading coefficient and the odd degree combine to tell you the end value of f(x) will have the opposite sign of the end value of x.

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If the degree were even, the end value of f(x) would have the same sign as the leading coefficient, regardless of the sign of the end value of x.