Question

What is the end behavior of function h(z) = 2(2-3)³ as z approaches negative infinity? As z approaches positive infinity, h(z) approaches _________.

1) 2
2) 0
3) 1
4) cannot be determined

Answer 1

The function h(z) = 2(2-3)³ is a constant and doesn't change with the value of z, so as z approaches positive infinity, h(z) approaches -2 which is none of the given options therefore the correct choice is 'cannot be determined'.

Step-by-step explanation:

The end behavior of the function h(z) = 2(2-3)³ as z approaches negative infinity cannot impact the function's value since the function is essentially a constant. The term (2-3)³ simplifies to (-1)³ which is -1, and when multiplied by 2, it gives -2. Hence, the function's value is -2 regardless of the value of z. So, as z approaches positive infinity, h(z) approaches -2, not any of the options given (1) 2, (2) 0, (3) 1, (4) cannot be determined. However, if we have to choose from the given options, the correct approach would be option (4) cannot be determined, because the value (-2) is not listed as a choice.