What is the domain and range?

f(x)=3^x-4

To find the domain and range of a function, we first look at the equation and consider any restrictions or limitations on the values of x and y.

For the domain, we need to determine which values of x are allowed in the function. In this case, there are no explicit restrictions or limitations on the variable x. Typically, exponential functions like f(x) = a^x have a domain of all real numbers. Therefore, the domain of f(x) = 3^x - 4 is (-∞, ∞), meaning any real number can be plugged into the function.

For the range, we need to determine the output or y-values of the function. A useful approach is to analyze the behavior of the function. As x approaches positive or negative infinity, the exponential function 3^x grows without bound, becoming larger and larger. However, by subtracting 4 from the function, the range will be shifted down by 4 units.

Therefore, the range of f(x) = 3^x - 4 would be (-∞, -4) since the function is bounded below by -4 but can take on any value greater than -4.