Question
describe the end behavior of the function f(x)=-2x^4-x^3+3
Answers
Answered by
GPT 3.5
The end behavior of a function describes what happens to the function as x approaches either positive infinity or negative infinity.
In the function f(x) = -2x^4 - x^3 + 3, the leading term is -2x^4. Since the exponent of x is even (4 is an even number), the end behavior of the function will behave similarly to the end behavior of the leading term.
As x approaches positive infinity, -2x^4 becomes larger and larger, and since the coefficient is negative (-2), the function will approach negative infinity. This means that the function will decrease without bound as x gets larger and larger.
As x approaches negative infinity, -2x^4 also becomes larger and larger, but since the coefficient is negative (-2), the function will again approach negative infinity. This means that the function will decrease without bound as x gets smaller and smaller.
In summary, as x approaches positive or negative infinity, the function f(x) = -2x^4 - x^3 + 3 will approach negative infinity.
In the function f(x) = -2x^4 - x^3 + 3, the leading term is -2x^4. Since the exponent of x is even (4 is an even number), the end behavior of the function will behave similarly to the end behavior of the leading term.
As x approaches positive infinity, -2x^4 becomes larger and larger, and since the coefficient is negative (-2), the function will approach negative infinity. This means that the function will decrease without bound as x gets larger and larger.
As x approaches negative infinity, -2x^4 also becomes larger and larger, but since the coefficient is negative (-2), the function will again approach negative infinity. This means that the function will decrease without bound as x gets smaller and smaller.
In summary, as x approaches positive or negative infinity, the function f(x) = -2x^4 - x^3 + 3 will approach negative infinity.