#### Answer

$\delta=0.1$

#### Work Step by Step

We see from the graph that in order for $f(x)$ to be within $\epsilon=0.15$ of $L=7.5$, we must have
$$-3.1 \lt x \lt -2.9.$$
Subtracting $-3$ from all three sides gives
$$-0.1 \lt x-(-3) \lt 0.1.$$
Hence for $\delta = 0.1$,
$$0 \lt |x-(-3)| \lt \delta \implies 0 \lt |f(x)-7.5| \lt \epsilon.$$