f(x) = -8x4 – 3x + 2
1. Given the function above, what is the right end behavior?
2. Given the function above, what is the left end behavior?
3. Given the function above, what is the maximum number of turns?
To determine the right and left end behavior, as well as the maximum number of turns for the given function f(x) = -8x^4 – 3x + 2, we need to analyze the degree of the polynomial function.
1. Right End Behavior:
The right end behavior can be determined by examining the leading term of the polynomial. In this case, the leading term is -8x^4. Since the degree (power of x) is even and the leading coefficient (-8) is negative, the right end behavior of the function is that it approaches negative infinity as x approaches positive infinity.
2. Left End Behavior:
Similarly, the left end behavior is determined by examining the leading term. As x approaches negative infinity, the right end behavior of the function is that it approaches negative infinity as x approaches negative infinity.
3. Maximum Number of Turns:
The maximum number of turns is determined by the degree of the polynomial function. In this case, the degree is 4. A polynomial of degree 4 can have a maximum of n – 1 turns, where n is the degree of the polynomial. Therefore, the maximum number of turns for this function is 4 – 1 = 3.
To summarize:
1. The right end behavior of the function is that it approaches negative infinity as x approaches positive infinity.
2. The left end behavior of the function is that it approaches negative infinity as x approaches negative infinity.
3. The maximum number of turns for the function is 3.