Graph y = x3 + 6x2 + 8x and describe the end behavior. (1 point)
The end behavior is down and up
The end behavior is down and up
The end behavior is up and down
The end behavior is up and down.
The correct answer is: The end behavior is up and down.
To graph the function y = x^3 + 6x^2 + 8x and understand its end behavior, we can follow these steps:
Step 1: Determine the degree of the polynomial function. In this case, the highest exponent of x is 3. Therefore, the degree of the function is 3.
Step 2: Use the degree and the leading coefficient to determine the end behavior.
- If the degree is odd (in this case, 3), and the leading coefficient is positive, the end behavior is: as x approaches negative infinity, y approaches negative infinity, and as x approaches positive infinity, y approaches positive infinity. This means the graph is angled downwards on the left side and angled upwards on the right side.
- If the degree is odd (in this case, 3), and the leading coefficient is negative, the end behavior is: as x approaches negative infinity, y approaches positive infinity, and as x approaches positive infinity, y approaches negative infinity. This means the graph is angled upwards on the left side and angled downwards on the right side.
- If the degree is even (even powers of x), regardless of the leading coefficient, the end behavior is: as x approaches negative infinity, and as x approaches positive infinity, y approaches positive infinity. This means the graph is always angled upwards on both sides.
In the given function, the degree is odd (3), and the leading coefficient is 1 (implied). Therefore, the end behavior is down and up. This means that as x approaches negative infinity, y approaches negative infinity, and as x approaches positive infinity, y approaches positive infinity.