use the following graph of the function f to determine the largest value of δ > 0 such that if |x - 5| < δ…

Explanation:

Step1: Analyze left - hand side distance

We want to find $\delta$ such that $|x - 5|<\delta$ implies $|f(x)-5|<0.8$. Looking at the left - hand side of $x = 5$, when $x = 3.9$, $f(x)=4.2$. The distance from $x = 5$ to $x = 3.9$ is $|5 - 3.9|=1.1$.

Step2: Analyze right - hand side distance

Looking at the right - hand side of $x = 5$, when $x = 5.6$, $f(x)=4.2$. The distance from $x = 5$ to $x = 5.6$ is $|5.6 - 5| = 0.6$.

Step3: Determine $\delta$

We take the minimum of these two distances. Since $\delta$ must satisfy the condition for both sides, $\delta=\min{1.1,0.6}$.

Answer:

$0.6$