what is the domain and range of -4 + 3^(x+2)

There is no reason why any old x can not be used. Therefore domain is all real values of x.

However how could this function ever have a value less than negative 4? The second term is always positive, although it can be pretty small if x is a large negative number. Like 3^-50 = 1/3^50 which is pretty tiny.

so the range is y>-4

yes

Thanks Damon!

To find the domain and range of the function -4 + 3^(x + 2), we need to consider the restrictions on the input (x) values and the corresponding output (y) values.

1. Domain: The domain refers to all possible values of x for which the function is defined. In this case, the function involves an exponential term, 3^(x + 2). Since exponential functions are defined for all real numbers, there are no restrictions on the domain in this case. Therefore, the domain of the function is (-∞, ∞).

2. Range: The range represents all possible values of y (output) that the function can take. To determine the range, we need to examine the behavior of the exponential function. As x increases without bound (x → ∞), the value of 3^(x + 2) also increases without bound. Conversely, as x decreases without bound (x → -∞), the value of 3^(x + 2) approaches zero but never reaches it. Therefore, the range of the function is (-∞, ∞), indicating that it can take on any real value.

In conclusion, the domain and range of the function -4 + 3^(x + 2) are both (-∞, ∞).