f(x) = log₂(-x)
Reflect base-2 log about the y-axis
The given function is:
f(x) = log₂(-x)
To find the domain of this function, we need to consider the value of x that makes the argument of the logarithmic function non-negative. Since the base of the logarithmic function is 2, the argument of the logarithmic function should be positive. So,
-x > 0
Multiplying both sides by -1, we get:
x < 0 Therefore, the domain of the given function is all negative real numbers. That is, Domain: (-∞, 0) To find the range of this function, we need to analyze the behavior of the logarithmic function. The logarithmic function is defined only for positive values of its argument. Therefore, we need to look at the behavior of the function as x approaches zero from the left-hand side (i.e., x → 0−). As x approaches zero from the left, -x approaches 0 from the right and thus, the argument of the logarithmic function approaches zero from the right as well. The logarithmic function has an asymptotic behavior when its argument approaches zero from the right. That is the logarithmic function approaches negative infinity but never touches it. Therefore, the range of the given function is all negative real numbers. That is, Range: (-∞, 0)
More Answers:
Analyzing The Function F(X) = -Log₂(-X): Domain, Intercepts, Intervals, Concavity, And AsymptotesLogarithmic Functions: The Formula For F(X) With Base 2.
The Negative Base 2 Logarithm Function – Domain, Range, And Graph