Which describes the end behavior of the graph of the function f(x)=-2x^3-5x^2+x?
a. f(x) approaches infinity as x approaches negative infinity and f(x) approaches infinity as x approaches infinity
b. f(x) approaches negative infinity as x approaches negative infinity and f(x) approaches negative infinity as x approaches infinity
c. f(x) approaches infinity as x approaches negative infinity and f(x) approaches negative infinity as x approaches infinity
d. f(x) approaches negative infinity as x approaches negative infinity and f(x) approaches infinity as x approaches infinity
I do not understand end behavior and my lesson does not explain it very well. I also have no textbook for this class. Help is greatly appreciated. Thanks!
C) f(x) approaches infinity as x approaches negative infinity and f(x) approaches negative infinity as x approaches infinity
end behavior is when x becomes very large (approaching infinity) in the positive and negative directions
the behavior is driven by the term with the largest exponent ... in this case, the x cubed term
the odd power means that x^3 has the same sign as x
the negative coefficient (-2) changes the sign, so that at the ends, f(x) has the opposite sign of x
read the answers carefully, and one will fit the bill
Pleaseee
Is it d?
I am pretty sure it's right can you please check?
End behavior refers to what happens to the function as x approaches negative infinity (left-hand side) and as x approaches positive infinity (right-hand side). To determine the end behavior of a function, we can look at the leading term with the highest degree.
In this case, the function f(x) = -2x^3 - 5x^2 + x has a leading term of -2x^3. Since the leading term has an odd degree and a negative coefficient (-2), the end behavior can be determined as follows:
- As x approaches negative infinity, the leading term (-2x^3) becomes more and more negative. As a result, f(x) approaches negative infinity. Therefore, the function approaches negative infinity as x approaches negative infinity.
- As x approaches positive infinity, the leading term (-2x^3) becomes more and more positive. As a result, f(x) approaches positive infinity. Therefore, the function approaches positive infinity as x approaches positive infinity.
Therefore, the correct answer is: a. f(x) approaches infinity as x approaches negative infinity and f(x) approaches infinity as x approaches infinity.
in d, are the signs for x and f(x) the same or different
did you read my first response/explanation?