Final answer:
A function with a horizontal asymptote at y=0 is represented by a horizontal line, which is denoted by the slope being zero in the linear equation y = mx + b. The only function that fits this description is y = 0, as it has no slope and lies on the x-axis.
Step-by-step explanation:
The question is asking which function has the x-axis as its horizontal asymptote, which means we are looking for a function where as x approaches infinity, the value of y approaches 0.
From the options and information given, a function with a horizontal asymptote at y=0 would have the characteristics of a horizontal line graph as mentioned in the text. A horizontal line occurs when the slope (b) is zero because the equation of a straight line is y = mx + b, where m is the slope and b is the y-intercept.
Option (b) y = 0 is the only equation that represents a horizontal line, which means it is the function that has the x-axis as its horizontal asymptote.
This is because the slope is 0 and there is no rise over run, leading to a straight horizontal line that coincides with the x-axis.
Thus, as x approaches any real number value, the value of y remains constant at 0, creating a horizontal asymptote at y=0.