The graph of y = log_10(x) in the xy-plane intersects the y-axis at what value of y?
The graph of y = log_10(x) does not intersect the y-axis.
The function y = log_10(x) is defined only for positive values of x, meaning it does not have any points on the y-axis where x equals zero. Therefore, it cannot intersect the y-axis at any value of y.
At y = 0, the corresponding value of x would need to be 10^0, which equals 1. This point lies on the graph but does not indicate an intersection with the y-axis, as the graph is undefined for x = 0.
This value suggests that there is a point on the y-axis at y = 110, which is incorrect. The graph never touches the y-axis since logarithmic functions are only defined for positive x values.
While the graph has a point at (1, 0) where y = log_10(1), this does not mean it intersects the y-axis. The function does not exist at x = 0, thus it cannot intersect the y-axis at y = 1.
The point (10, 1) is on the graph, indicating that when x = 10, y = 1. However, this does not imply an intersection with the y-axis, as the function remains undefined for x = 0.
The logarithmic function y = log_10(x) lacks intersection with the y-axis because it is only defined for positive x values. All provided options suggest values for y at which the function cannot cross the y-axis, reinforcing the conclusion that the graph does not intersect this axis at any point.
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