Question

what is the average rate of change between: x = 1 and x = 2? x = 2 and x = 3? x = 3 and x = 4? done

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \(y = f(x)\) over the interval \([a,b]\) is \(\frac{f(b)-f(a)}{b - a}\).

Step2: Find values for \(x = 1\) and \(x = 2\)

From the graph, when \(x = 1\), \(y=2\) (since \(f(1)=2\)), and when \(x = 2\), \(y = 4\) (since \(f(2)=4\)).

$$ \frac{f(2)-f(1)}{2 - 1}=\frac{4 - 2}{1}=2 $$

Step3: Find values for \(x = 2\) and \(x = 3\)

When \(x = 2\), \(y = 4\) (\(f(2)=4\)), and when \(x = 3\), \(y = 8\) (\(f(3)=8\)).

$$ \frac{f(3)-f(2)}{3 - 2}=\frac{8 - 4}{1}=4 $$

Step4: Find values for \(x = 3\) and \(x = 4\)

When \(x = 3\), \(y = 8\) (\(f(3)=8\)), and when \(x = 4\), \(y = 16\) (\(f(4)=16\)).

$$ \frac{f(4)-f(3)}{4 - 3}=\frac{16 - 8}{1}=8 $$

Answer:

\(2\)
\(4\)
\(8\)