What is the domain and range of f(x)=3^x-4
To find the domain and range of the function f(x) = 3^x - 4, we need to consider two things: the domain restrictions and the range possibilities.
First, let's discuss the domain restrictions. The function f(x) = 3^x - 4 involves raising 3 to the power of x, which means x can be any real number. Therefore, the domain of f(x) is all real numbers (-∞, +∞).
Next, let's determine the range of the function. Since 3^x is always positive for any real value of x, the -4 is the only component that can affect the range. By subtracting 4 from the exponential function, we shift the graph down by 4 units. Thus, the range of f(x) will be all real numbers less than or equal to -4 (-∞, -4].
In summary, the domain of f(x) = 3^x - 4 is all real numbers (-∞, +∞), and the range is all real numbers less than or equal to -4 (-∞, -4].