Question

The function ƒ is given by f(x)=-2x⁷+5x⁴+6x²-3. Which of the following correctly describes the end behavior of f as the input values increase without bound?

a. limₓ→[infinity] f(x)= -[infinity]
b. limₓ→-[infinity] f(x)= [infinity]
c. limₓ→-[infinity] f(x)= [infinity]
d. limₓ→[infinity] f(x)= [infinity]

Answer 1

The function ƒ(x) = -2x⁷ + 5x⁴ + 6x² - 3 approaches negative infinity as the input values increase without bound.

Step-by-step explanation:

The end behavior of the function ƒ(x) = -2x⁷ + 5x⁴ + 6x² - 3 as the input values increase without bound can be determined by looking at the leading term of the function. The leading term is the term with the highest degree, which in this case is -2x⁷. Since the coefficient of the leading term is negative, the function will approach negative infinity as the input values increase without bound. Therefore, the correct answer is a. limₓ→[infinity] f(x) = -[infinity].