Question

Find the average rate of change of each function over the interval [0,3]. Match each representation with its respective average rate of change.

Answer 1

Remember that to determine the average rate of change over an interval, you can use the formula f(b) - f(a) / b - a. Remember that we have to find the average rate of change over the interval [0, 3].

(1) Given our table, we know that g(3) = 5, and and g(0) = - 13. Respectively b = 3, and a = 0. Let's substitute,

$5 - (- 13) / 3 - 0 \\= 5 + 13 / 3\\= 18 / 3 = 6$

The average rate of change of the table is hence 6.

(2) Here we are given that our function has an x-intercept of (3,0), and a y-intercept of (0,6). Therefore p(3) = 0, and p(0) = 6. And of course b = 3, and a = 0,

$0 - 6 / 3 - 0\\= - 6 / 3 = - 2$

The average rate of change of 'function p' is - 2.

(3) If you take a look at the graph, f(3) = 5, and f(0) = - 4. Let's substitute,

$5 - (-4) / 3 - 0\\= 5 + 4 / 3 = 9 / 3\\= 3$

Hence the average rate of change of the graph is 3.

(4) Knowing the equation we can solve for r(3) and r(0) by plugging in 3 and 0 for x. Let's do it,

r(3) = (3)² + 2(3) - 5 = 9 + 6 - 5 = 10,

r(0) = (0)² + 2(0) - 5 = - 5

Now let's substitute into the formula f(b) - f(a) / b - a,

$10 - (- 5) / 3 - 0\\= 10 + 5 / 3 = 15 / 3\\= 5$

The average rate of change of the equation is 5.