Answer: Linear
Explanation:
Since the difference between consecutive values of f(x) is constant, this suggests that the function could be linear. To confirm this, we can calculate the differences between consecutive values:f(1) - f(0) = -15 - (-18) = 3
f(2) - f(1) = -12 - (-15) = 3
f(3) - f(2) = -9 - (-12) = 3
f(4) - f(3) = -6 - (-9) = 3
Since the differences are constant and equal to 3, this confirms that the function is linear.
To find the equation of the linear function, we can use the slope-intercept form of a linear equation:
y = mx + bwhere m is the slope and b is the y-intercept.
We can use the first two points (0, -18) and (1, -15) to find the slope:
m = (change in y) / (change in x) = (-15 - (-18)) / (1 - 0) = 3
Now we can use the slope and one of the points to find the y-intercept:
y = mx + b
-18 = 3(0) + b
b = -18
Therefore, the equation of the linear function is:
f(x) = 3x - 18
So the function type that could represent the values in the table is linear.