f(x) = -log₂x
Reflect base-2 log across the x-axis
The function f(x) = -log₂x can be interpreted as the negative base 2 logarithm of x. This function has a domain of x > 0, since taking the logarithm of a negative number or zero is not defined.
To find the range of the function, we can note that as x approaches infinity, the logarithm approaches zero. Therefore, the range of f(x) is (-∞, 0). In other words, the function takes on all negative values and never reaches zero or any positive values.
Additionally, since the base of the logarithm is 2, we can use the change of base formula to rewrite the function as:
f(x) = -log₂x = -(lnx / ln2)
This form of the function can be useful for evaluating it on a calculator or computer, since the natural logarithm (ln) is often readily available.
As for the graph of the function, we can see that it is a decreasing function that approaches negative infinity as x approaches zero, and approaches zero as x approaches infinity. The graph is also defined for all values of x > 0, since the inverse of the logarithm function has a vertical asymptote at zero.
More Answers:
The Domain, Range, Vertical Asymptote, And Symmetry Of F(X) = Log₂(X-2)Analyzing The Function F(X) = -Log₂(-X): Domain, Intercepts, Intervals, Concavity, And Asymptotes
Logarithmic Functions: The Formula For F(X) With Base 2.