The correct statement about the graph function f(x) = log₂x is; The graph has an asymptote of x = 0 and is negative over the interval (0, 1).
We are given the function;
f(x) = log₂x
Now, at f(0), we have;
f(x) = log₂(0)
f(x) = log 0/log 2
f(x) = -∞/0.3010
Thus, since the value is infinity, then we can say that a straight line constantly approaches the curve but does not meet at any infinite distance and as such there is an asymptote at x = 0 and it is negative over the interval (0, 1).
The missing options are;
A. The graph has an asymptote of x = 0 and is positive over the interval (0, 1).
B. The graph has an asymptote of x = 0 and is negative over the interval (0, 1).
C. The graph has an asymptote of y = 0 and is decreasing as x approaches positive infinity.
D. The graph has an asymptote of y = 0 and is increasing as x approaches positive infinity.
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