Final answer:
The average rate of change of the function f(x) = x² − 4 over the interval [−5, −2] is −7. The correct option is C. −7
Step-by-step explanation:
To determine the average rate of change of the function f(x) = x² − 4 over the interval [−5, −2], we use the formula for average rate of change which is:
Average Rate of Change = ∆f(x) / ∆x = (f(x2) - f(x1)) / (x2 - x1)
Here, x1 = −5 and x2 = −2. So we calculate this as follows:
f(−5) = (−5)² − 4 = 25 − 4 = 21
f(−2) = (−2)² − 4 = 4 − 4 = 0
The difference in function values, ∆f(x), is f(−2) - f(−5) = 0 - 21 = −21.
The difference in x values, ∆x, is −2 − (−5) = 3.
To determine the average rate of change of the function f(x) = x^2 - 4 over the interval [-5, -2], we need to find the difference in the function values at the endpoints of the interval and divide it by the difference in the x-values.
First, we calculate the function values:
f(-5) = (-5)^2 - 4 = 25 - 4 = 21
f(-2) = (-2)^2 - 4 = 4 - 4 = 0
Next, we find the difference in the function values: 0 - 21 = -21
And the difference in the x-values: -2 - (-5) = 3
Finally, we divide the difference in function values by the difference in x-values: -21/3 = -7
Therefore, the average rate of change is −21 / 3, which simplifies to −7.
The correct option is C. −7