Question

Determine when y=-3((2)/(7))ˣ is positive, negative, increasing, or decreasing.

Answer 1

The given function is y = -3(2/7)^x. The function is positive for all even values of x and negative for all odd values of x. The function is increasing for all values of x.

Step-by-step explanation:

The given function is y = -3(2/7)^x.

1. Positive: The function will be positive when the value of x is even because any positive number raised to an even power will always result in a positive value. Therefore, the function is positive for all even values of x.
2. Negative: The function will be negative when the value of x is odd. This is because any positive number raised to an odd power will result in a negative value. Therefore, the function is negative for all odd values of x.
3. Increasing: The function is increasing for all values of x. This is because the base of the exponential function, 2/7, is between 0 and 1, which means that as the value of x increases, the function value will become smaller and smaller. This shows an increasing trend.
4. Decreasing: None of the above options mention the function being decreasing.