To find the range of the function f(x) = 3x + 2 over the interval -6 < x < 5, you would follow the steps below.
1. Calculate the value of the function at the lower end of the interval.
When you plug in x = -6 into the function, you would get:
f(-6) = 3*(-6) + 2
= -18 + 2
= -16
So, the minimum value of the function over the interval is -16.
2. Calculate the value of the function at the upper end of the interval.
When you plug in x = 5 into the function, you would have:
f(5) = 3*5 + 2
= 15 + 2
= 17
Therefore, the maximum value of the function over the interval is 17.
3. The range of the function over the given interval is the difference between the maximum and minimum values.
You can calculate this by subtracting the minimum value from the maximum value:
Range = max - min
= 17 - (-16)
= 17 + 16
= 33
Therefore, the range of the function f(x) = 3x + 2 over the interval -6 < x < 5 is 33.