The average rate of change of f(x) over the interval [-4,-1] is 2 , the value of f(-1) is 3 and value of f(-4) is -3 .
In the question ,
a linear graph of the function f(x) is given ,
we have to find the rate of change of the function f(x) ,
We know that the Rate Of Change of the function f(x) over interval [a,b] is calculated using the formula ;
Rate Of Change [tex]=[/tex] (f(b) - f(a))/(b - a)
the interval is [-4,-1] ,
So , a = -4 and b = -1 .
From the graph , the value of f(-1) is = 3 ,
and the value of f(-4) is = -3 ,
So , By the Rate Of Change formula ,
we get ,
Rate Of Change = (f(-1) - f(-4))/(-1 -(-4))
= (3 -(-3))/(-1 + 4)
= (3 + 3)/3
= 6/3
= 2
Therefore , the rate of change over the interval [-4,-1] is 2 .
The given question is incomplete , the complete question is
Calculate the average rate of change of f(x) (shown in the graph) over the interval [-4, -1] using the formula. The value of f(-1) is. The value of f(-4) is. The average rate of change of f(x) over the interval [-4, -1] is .
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