Question

Which graph shows the logarithmic function

f(x) = log0.5x ?


On a coordinate plane, a logarithmic functions intercepts the y-axis at (0, 1).

On a coordinate plane, a logarithmic function goes through (0, 2.5) and (1.5, 0).

Answer 1

The graph that shows the logarithmic function f(x) = log0.5x is the second one, which goes through (0, 2.5) and (1.5, 0). This is because the general form of a logarithmic function is f(x) = loga(x), where a is the base of the logarithm. In this case, the base of the logarithm is 0.5, so the function can be written as f(x) = log0.5(x). The second graph matches the given points and has the characteristic shape of a logarithmic function, with a vertical asymptote at x = 0 and a horizontal asymptote at y = 0.