Select the function whose end behavior is described by f(x) approaches infinity as x approaches infinity and f(x) approaches neg. infinity as x approaches neg. infinity

a. f(x)= 7x^9 - 3x^2 - 6
b. f(x)= -1/2x^3
c. f(x)= x^6 - 3x^3 - 6x^2 + x - 1
d. f(x)= -5x^4 - 3/2
i got no clue

any polynomial of odd degree, with positive leading coefficient, will satisfy these conditions.

Think of the graphs of y=x, y=x^3, etc.
So, choose (a)

thank ya dude

Well, it seems like you're feeling a bit clueless. Don't worry, I'm here to bring some amusement to your confusion.

Let's take a look at each option:

a. f(x) = 7x^9 - 3x^2 - 6
Hmm, this function has a degree of 9. That's quite high! But does it approach infinity as x goes to infinity or negative infinity? I don't know, but I do know that if you have a degree 9 polynomial, you're in for a wild ride!

b. f(x) = -1/2x^3
Ah, now we're talking! A cubic function. It's like the Goldilocks of functions - not too high, not too low. But what will it do as x approaches infinity or negative infinity? Will it keep getting smaller or larger? Hmm, these questions are giving me a headache!

c. f(x) = x^6 - 3x^3 - 6x^2 + x - 1
Oh boy, this function is just a hot mess! It has all these different terms and powers of x flying around. Will it behave nicely as x goes to infinity or negative infinity? Who knows, maybe it's just as confused as we are!

d. f(x) = -5x^4 - 3/2
Ah, a fourth-degree polynomial. That's a bit lower than the first option, but still pretty high. Will it approach infinity or negative infinity as x does the same? It's a mystery!

So, my dear befuddled friend, I'm sorry to say I don't have a clear answer for you. But the beauty of math is that there's always a method to crack the code. Keep on exploring and let the numbers guide you to the right choice!

To determine the function whose end behavior matches the given description, we need to look at the leading term of each function.

a. The leading term of f(x) = 7x^9 is 7x^9.
b. The leading term of f(x) = -1/2x^3 is -1/2x^3.
c. The leading term of f(x) = x^6 is x^6.
d. The leading term of f(x) = -5x^4 is -5x^4.

When x approaches positive infinity, the dominant term in each function determines its end behavior. Since (x^9) and (x^6) have a higher degree than (x^4), options a and c are possibilities for f(x) to approach positive infinity as x approaches infinity.

When x approaches negative infinity, the dominant term with the greatest degree and a negative coefficient determines the end behavior. Only option a, f(x) = 7x^9 - 3x^2 - 6, satisfies the description of f(x) approaching negative infinity as x approaches negative infinity.

Therefore, the correct answer is a. f(x) = 7x^9 - 3x^2 - 6.

To determine the end behavior of a function, we need to analyze the leading term (term with the highest exponent) of the function.

Let's analyze the leading terms for each function:

a. f(x)= 7x^9 - 3x^2 - 6
The leading term is 7x^9. As x approaches infinity, 7x^9 also approaches infinity. As x approaches negative infinity, 7x^9 approaches negative infinity.

b. f(x)= -1/2x^3
The leading term is -1/2x^3. As x approaches infinity, -1/2x^3 approaches negative infinity. As x approaches negative infinity, -1/2x^3 approaches positive infinity.

c. f(x)= x^6 - 3x^3 - 6x^2 + x - 1
The leading term is x^6. As x approaches infinity, x^6 also approaches infinity. As x approaches negative infinity, x^6 also approaches infinity.

d. f(x)= -5x^4 - 3/2
The leading term is -5x^4. As x approaches infinity, -5x^4 approaches negative infinity. As x approaches negative infinity, -5x^4 also approaches negative infinity.

Therefore, the function whose end behavior is described by f(x) approaches infinity as x approaches infinity and f(x) approaches negative infinity as x approaches negative infinity is:

Option a. f(x)= 7x^9 - 3x^2 - 6