To find f(13) for the linear function, we first calculate the slope using points from the table. Then we use the slope and a point to derive the equation of the line in slope-intercept form and finally substitute x = 13 into the equation to obtain f(13) = 34/3.
To determine the value of f(13) for a linear function given specific values, we need to find the slope (m) of the line and use it to extend the pattern. The slope can be calculated using two points from the table:
For x = -3, f(x) = -10
For x = 3, f(x) = -2
Using these points, the slope m is calculated as:
m = (f(3) - f(-3)) / (3 - (-3))
m = (-2 - (-10)) / (3 - (-3))
m = (8) / (6)
m = 4/3
Now we use one of the points and the slope to write the equation of the line in slope-intercept form y = mx + b. We can use the point (3, -2):
-2 = (4/3)(3) + b
-2 = 4 + b
b = -2 - 4
b = -6
Therefore, the equation of the line is:
y = (4/3)x - 6
To find f(13), we plug x = 13 into the equation:
f(13) = (4/3)(13) - 6
f(13) = 52/3 - 6
f(13) = 52/3 - 18/3
f(13) = 34/3
Hence, the value of f(13) is 34/3, which corresponds to option D.