f(x)= log2 (x-1).The vertical asymptote of the function f(x) has equation:?
You should know that we can only take logs of positive numbers, so
x-1 > 0
x > 1
so the vertical asymptote is x = 1
found it! :)
thx!
To find the vertical asymptote of the function f(x) = log₂(x - 1), we need to consider the behavior of the function as x approaches certain values.
The vertical asymptote occurs when the function approaches positive or negative infinity. In this case, the function f(x) is a logarithmic function, which means it is undefined for non-positive numbers and the base of the logarithm should be positive.
In our function f(x) = log₂(x - 1), we have a restriction that x - 1 > 0 in order for the logarithm to be defined. Solving for x, we find that x > 1, which means the function f(x) is defined for x values greater than 1.
However, as x approaches 1 from the right (x → 1+), the function gets arbitrarily close to negative infinity. Therefore, the vertical asymptote of f(x) occurs at x = 1.
In conclusion, the equation of the vertical asymptote for the function f(x) = log₂(x - 1) is x = 1.