Final answer:
To find a function g(x) with x-intercepts at (1/2, 0) and (6, 0), we can use the slope-intercept form y = mx + b. Plugging in the values of (1/2, 0) into the equation y = mx + b, we can solve for the y-intercept, b. Therefore, the equation of the line passing through the two given points is y = 0.
Step-by-step explanation:
To find a function g(x) with x-intercepts at (1/2, 0) and (6, 0), we can use the fact that x-intercepts occur when the value of the function is equal to zero. We can start by finding the equation of the line passing through the two given points using the slope-intercept form, y = mx + b.
Using the given points (1/2, 0) and (6, 0), we can determine the slope, m, as 0, since the y-coordinates of both points are equal to zero. Plugging in the values of (1/2, 0) into the equation y = mx + b, we can solve for the y-intercept, b, which turns out to be 0 as well. Therefore, the equation of the line passing through the two given points is y = 0.