the graph shows the function $f(x)$. which value is closest to the average rate of change from $x = 1$ to $x…
the graph shows the function $f(x)$. which value is closest to the average rate of change from $x = 1$ to $x = 4$? -3.5 -2.3 -1.4 -0.3
Answer
Answer:
-1.4
Explanation:
Step1: Recall average - rate - of - change formula
The average rate of change of a function $y = f(x)$ from $x=a$ to $x = b$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 1$ and $b=4$.
Step2: Estimate function values from graph
From the graph, when $x = 1$, $f(1)\approx7$. When $x = 4$, $f(4)\approx2$.
Step3: Calculate average rate of change
$\frac{f(4)-f(1)}{4 - 1}=\frac{2 - 7}{3}=\frac{-5}{3}\approx - 1.67$. The value closest to $-1.67$ among the options is $-1.4$.