the graph of a logarithmic function is shown below.\nwhat is the domain of the function?

Explanation:

Step1: Recall domain of logarithmic functions

The general form of a logarithmic function ( y = \log_b(x - h) + k ) has a domain determined by the argument ( x - h > 0 ), i.e., ( x > h ). From the graph, we observe the vertical asymptote (the point where the function approaches but never touches) is at ( x = 0 ) (or slightly to the right, but from the graph, the function starts increasing from ( x > 0 )? Wait, no, looking at the graph, the curve starts at a point where ( x ) is just greater than ( 0 )? Wait, no, the graph shows that the function is defined for ( x > 0 )? Wait, no, looking at the x - axis, the graph starts after ( x = 0 )? Wait, no, the graph crosses the x - axis? Wait, no, the graph is a logarithmic function. Wait, the standard logarithmic function ( y=\log_b x ) has domain ( x>0 ). But in the graph, we can see that the function starts at ( x = 0 )? Wait, no, the graph has a vertical asymptote? Wait, looking at the graph, the leftmost point of the curve is at ( x = 0 )? Wait, no, the curve starts at ( x = 0 ) (the y - axis) and goes to the right. Wait, actually, from the graph, we can see that the function is defined for all ( x ) values greater than ( 0 )? Wait, no, wait the graph: the curve starts at ( x = 0 ) (the point where ( x = 0 ), ( y=-1 )) and then increases. Wait, but for a logarithmic function, the argument must be positive. Wait, maybe the function is ( y=\log_b(x) + c ). The domain of ( y = \log_b(x) ) is ( x>0 ). But in the graph, the function is defined for ( x>0 )? Wait, no, looking at the x - axis, the graph starts at ( x = 0 ) (the y - axis) and goes to the right. Wait, maybe the vertical asymptote is at ( x = 0 ), so the domain is all real numbers greater than ( 0 ). Wait, but let's check the graph again. The graph is a logarithmic curve, and we can see that the function exists for ( x>0 ) (since to the left of ( x = 0 ), there is no graph). So the domain is all real numbers ( x ) such that ( x>0 )? Wait, no, wait the graph: the curve starts at ( x = 0 ) (the point (0, - 1)) and then increases. Wait, maybe the vertical asymptote is at ( x = 0 ), so the domain is ( x>0 )? Wait, no, maybe I made a mistake. Wait, the standard logarithmic function ( y = \log_b(x) ) has domain ( x>0 ). But in the graph, we can see that the function is defined for ( x>0 ). Wait, but looking at the x - axis, the graph is present for ( x>0 ). So the domain is all real numbers greater than ( 0 ), i.e., ( x\in(0,+\infty) ) or in interval notation, ( (0, \infty) ). Wait, but maybe the vertical asymptote is at ( x = 0 ), so the domain is ( x>0 ).

Step2: Determine the domain from the graph

From the graph, we observe that the function is defined for all ( x ) values where ( x>0 ). This is because the logarithmic function (from the shape of the graph) has a vertical asymptote at ( x = 0 ), and the function is defined for all ( x ) to the right of this asymptote. So the domain is all real numbers greater than ( 0 ).

Answer:

The domain of the function is all real numbers greater than ( 0 ), which in interval notation is ( (0, \infty) ) (or ( x>0 )).