a) To find g(-6), we can estimate the value of g(-6) by finding the equation of the line that passes through the points (-5,0) and (-3,-2). To do this, we can use the slope-intercept formula:
y - y1 = m(x - x1)
where m is the slope of the line and (x1, y1) is one of the points on the line.
m = (y2 - y1) / (x2 - x1) = (-2 - 0) / (-3 - (-5)) = -1/2
Using the point-slope formula with (x1, y1) = (-5, 0), we get:
y - 0 = (-1/2)(x - (-5))
y = (-1/2)x + 5/2
Therefore, g(-6) is approximately equal to g(-5), which we can find by substituting x = -5 into the equation:
g(-5) = (-1/2)(-5) + 5/2 = 5/2
So, g(-6) is approximately equal to 5/2.
b) To find g(4), we look for the value of y when x is 4. From the table, we can see that when x is 4, g(x) is equal to -6. Therefore, g(4) = -6.
c) To find the value of x when g(x) is 0, we look for the row where g(x) is 0. From the table, we can see that when x is -5, g(x) is equal to 0. Therefore, x = -5 when g(x) = 0.