Question

For the function f(x) = -ax^4 + bx^3 + c, if a > 0, which of the following describes the end behavior of f(x)?

a) A. f(x) approaches positive infinity
b) B. f(x) approaches negative infinity
c) C. f(x) approaches c
d) D. f(x) approaches 0

Answer 1

For the function f(x) = -ax^4 + bx^3 + c with a > 0, the end behavior is that f(x) approaches negative infinity due to the dominant x^4 term with a negative coefficient.

Step-by-step explanation:

The end behavior of the function f(x) = -ax^4 + bx^3 + c, where a > 0, is determined by the highest degree term, which in this case is -ax^4. Since a is positive, the coefficient of the x^4 term is negative. This means as x goes to positive or negative infinity, the x^4 term will dominate and the function will approach negative infinity. So, the correct description of the end behavior is B. f(x) approaches negative infinity.