Question

the function ( y = f(x) ) is graphed below. what is the average rate of change of the function ( f(x) ) on the interval ( -1leq xleq0 )?

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \(y = f(x)\) on the interval \([a,b]\) is given by \(\frac{f(b)-f(a)}{b - a}\). Here, \(a=-1\) and \(b = 0\).

Step2: Identify \(f(-1)\) and \(f(0)\) from the graph

From the graph, when \(x=-1\), \(f(-1)=-4\) and when \(x = 0\), \(f(0)=-8\).

Step3: Substitute values into the formula

Substitute \(a=-1\), \(b = 0\), \(f(a)=-4\) and \(f(b)=-8\) into \(\frac{f(b)-f(a)}{b - a}\).

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Answer:

\(-4\)