Question
f(x) = log2x
Answers
GPT 3.5
The function f(x) = log2x represents the logarithm of x to the base 2. This means that for any positive real number x, f(x) gives the exponent to which 2 must be raised to obtain x.
For example, if we evaluate f(4), we get log24 = 2, because 2 raised to the power of 2 equals 4.
The domain of this function is all positive real numbers greater than 0, since logarithms are defined only for positive numbers.
The range of the function is all real numbers, since the logarithm can yield negative and positive values depending on the input.
The graph of f(x) = log2x is a monotonically increasing curve that passes through the point (1, 0) on the coordinate plane. As x increases, the value of the logarithm also increases, but at a decreasing rate.
To summarize:
- Domain: (0, +∞)
- Range: (-∞, +∞)
- Graph: Monotonically increasing curve passing through (1, 0)
For example, if we evaluate f(4), we get log24 = 2, because 2 raised to the power of 2 equals 4.
The domain of this function is all positive real numbers greater than 0, since logarithms are defined only for positive numbers.
The range of the function is all real numbers, since the logarithm can yield negative and positive values depending on the input.
The graph of f(x) = log2x is a monotonically increasing curve that passes through the point (1, 0) on the coordinate plane. As x increases, the value of the logarithm also increases, but at a decreasing rate.
To summarize:
- Domain: (0, +∞)
- Range: (-∞, +∞)
- Graph: Monotonically increasing curve passing through (1, 0)