#### Answer

$\delta =0.1$

#### Work Step by Step

We see from the graph that in order for $f(x)$ to be within $\epsilon=0.2$ of 6, we must have
$$4.9 \lt x \lt 5.1.$$
Subtracting 5 from all three sides gives
$$-0.1 \lt x-5 \lt 0.1.$$
Hence for $\delta = 0.1$, $$0 \lt |x-5| \lt \delta \implies 0 \lt |f(x)-6| \lt \epsilon.$$