Which of the following functions has the same end behavior as f(x)=ax^3+bx^2+cx+d?
a. −ax^2+bx+c
b. −ax^6
c. ax^4−bx^3+cx^2+dx+e
d. ax+b
can some body help me i am confused
ax^3 is an odd polynomial
so is ax
The other powers do not matter.
So, D
thank you
Of course! I'd be happy to help you out.
To determine the end behavior of a function, we are interested in how the function behaves as x approaches positive and negative infinity. The end behavior is determined by the leading term of the function, which is the term with the highest degree.
In this case, the given function is f(x) = ax^3 + bx^2 + cx + d. The leading term is ax^3, which has a degree of 3.
Now, let's compare the leading term of the given function to the leading terms of the answer choices to find the function with the same end behavior:
a. −ax^2 + bx + c
- The leading term is -ax^2, which has a degree of 2. Different degree from f(x).
- This option does not have the same end behavior as f(x).
b. −ax^6
- The leading term is -ax^6, which has a degree of 6. Different degree from f(x).
- This option does not have the same end behavior as f(x).
c. ax^4 − bx^3 + cx^2 + dx + e
- The leading term is ax^4, which has a degree of 4. Different degree from f(x).
- This option does not have the same end behavior as f(x).
d. ax + b
- The leading term is ax, which has a degree of 1. Different degree from f(x).
- This option does not have the same end behavior as f(x).
From the given answer choices, there is no function that has the same end behavior as f(x) = ax^3 + bx^2 + cx + d.
Therefore, the answer is none of the above.
I hope this clarifies your confusion! Let me know if there's anything else I can assist you with.