How many real zeroes does y = ( x + 8 )^3 + 9 have?
(1 point)
Responses
1
1
2
2
3
3
0
To determine the number of real zeroes of the equation y = (x + 8)^3 + 9, we need to analyze the equation and understand its properties.
First, notice that the equation is a cubic function due to the exponent of 3 on the x + 8 term. Cubic functions can have up to three real zeroes.
To find the number of real zeroes, we can assess the behavior of the function using the concept of end behavior. If the function increases indefinitely as x approaches negative infinity and decreases indefinitely as x approaches positive infinity, it means there are no real zeroes.
In this case, as the leading term of the equation is (x + 8)^3, it means that the function will increase indefinitely as x approaches negative infinity and decrease indefinitely as x approaches positive infinity.
Thus, the cubic function y = (x + 8)^3 + 9 has no real zeroes. The correct answer is 0.