Question 9

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 defined only for positive values of x. As x approaches zero, the function approaches negative infinity, and at x = 0, the function is undefined.

A) 110

This option is incorrect because the graph does not intersect the y-axis, and thus cannot have a y-value of 110 at that point. The logarithmic function is only defined for x > 0.

B) 1

This option is also incorrect. While log_10(10) equals 1, the function y = log_10(x) does not intersect the y-axis, meaning it cannot take the value of 1 at x = 0, where the y-axis is located.

C) 10

This option is incorrect as well. Although log_10(10) equals 1 and log_10(100) equals 2, the function still does not intersect the y-axis, meaning it cannot take the value of 10 at that point.

D) does not intersect the y-axis.

This is the correct option. The function y = log_10(x) is not defined for x = 0, hence it cannot intersect the y-axis.

Conclusion

The correct answer is that the graph of y = log_10(x) does not intersect the y-axis, as the function is undefined for x values less than or equal to zero. All other options incorrectly assume a y-value exists at the y-axis intersection, which is not possible for logarithmic functions.