Here is an Algebra two question that confuses me.
Question::
What are the left and right behaviors of
f(x)=-3x^5+x^4-9x
a.) Rises both to the right and to the left
b.)Falls both to the right and left
c.)Cannot be determined
d.)Rises to the right and falls to the left
e.)Rises to the left and falls to the right.
The help is much appreciated!
-Jazz
the answer is e if you have a graphing calculator you could put it in on that it helps for algebra
When x becomes very large, either positive or negative, the x^5 term will dominate the sum. So the left and right behaviors will mimic that of x^5. What happens when x goes to + or - infinity?
Therein lies your answer.
Bob's answer is correct. I didn't see the - sign in front of x^5. The polynomial approaches -x^5 when x -> + or - infinity.
Alright, I think I understand.
So would f(x)=-8x^6-x^3+-9
Rise to the right and fall to the left?
We were told a simple way to determine the behavior, but I have completely forgotten it.
To determine the left and right behaviors of a function, we need to analyze the leading term of the function.
In the given function f(x) = -3x^5 + x^4 - 9x, the leading term is -3x^5. The degree of this term is 5, which is an odd number.
When the degree is odd, the left and right behaviors of the function are different.
If the leading term has a positive coefficient (+3), the function rises to the left and falls to the right. But in this case, the leading term has a negative coefficient (-3), so we need to consider its impact on the function's behavior.
When the leading term has a negative coefficient (-3), the function rises to the right and falls to the left.
Therefore, the correct answer to the question is (d) Rises to the right and falls to the left.
To solve it mathematically, you can find the left and right behaviors by taking the limit of the function as x approaches positive and negative infinity. However, for this particular question, understanding the concept of odd degree leading term and its coefficient is sufficient to determine the answer.