Question 13

The graph of y = log_{10}x does not intersect the y-axis.

The graph of the function y = log_{10}x does not intersect the y-axis because the logarithmic function is undefined for x ≤ 0. Therefore, it does not have any points on the y-axis.

A) 01-Oct

This option is incorrect as it suggests a date, which is irrelevant in the context of the logarithmic function's intersection with the y-axis. The function does not have a defined value at x = 0 or for negative x-values.

B) 1

Option B is incorrect because the function y = log_{10}x does not produce a y-value of 1 when x is substituted with any value that would allow for an intersection with the y-axis. Since the function is undefined for x ≤ 0, this value cannot be achieved.

C) 10

This option is also incorrect. The function y = log_{10}x would only yield a value of 10 for a specific positive x-value (specifically, x = 10^10), but it does not intersect the y-axis at this point since it cannot take any values at x = 0.

D) It does not intersect the y-axis.

This answer correctly reflects the nature of the logarithmic function, which is undefined for x ≤ 0. Therefore, it does not have any intersection on the y-axis.

Conclusion

The correct answer is that the graph of y = log_{10}x does not intersect the y-axis, as it is undefined for any non-positive x-values. All other options misinterpret the behavior of the logarithmic function, failing to recognize that it cannot produce any valid output when x is less than or equal to zero.