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QuestionFind the average rate of change of YY over the interval [−4,4][-4, 4] using the values provided in the table.

Studdy Solution

STEP 1

Assumptions1. The given table represents a function f(x)f(x) at different points. . The average rate of change is calculated as the change in f(x)f(x) divided by the change in xx over the interval [−4,4][-4,4].

STEP 2

The formula for the average rate of change of a function over an interval [a,b][a,b] is given byAverage rate of change=f(b)−f(a)b−aAverage\, rate\, of\, change = \frac{f(b) - f(a)}{b - a}

STEP 3

From the table, we can see that f(−)=16f(-) =16 and f()=16f() =16. We can plug these values into the formula to find the average rate of change.
Average rate of change=f()−f(−)−(−)Average\, rate\, of\, change = \frac{f() - f(-)}{ - (-)}

STEP 4

Substitute the values of f(4)f(4) and f(−4)f(-4) into the formula.
Average rate of change=16−164−(−4)Average\, rate\, of\, change = \frac{16 -16}{4 - (-4)}

STEP 5

Calculate the numerator and denominator separately.
Average rate of change=08Average\, rate\, of\, change = \frac{0}{8}

STEP 6

Calculate the average rate of change.
Average rate of change=0Average\, rate\, of\, change =0The average rate of change of the function over the interval [−4,4][-4,4] is0.

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