Hi there!
We can go through each given function and determine whether the graph is its representation:
y = f(x) = log₂x. The graph pictured is logarithmic as it contains a vertical asymptote (discontinuity) at x = 0.
y = f(x) = x². This equation contains a parabolic shape. This is incorrect.
y = f(x) = 2ˣ. This equation is an exponential, increasing function. This is incorrect.
Another way to check would be to use the point on the graph (1, 0), and plug the corresponding x and y values into each function.
For example:
0 = log₂(1) is correct.
0 = (1)² is incorrect.
0 = 2¹ is incorrect.