Use the graph of $f$ to find $\delta$ such that if $0<|x-5|<\delta$, then $|f(x)-3|<0.6$

Question

I ended up with the answer $0<\delta<1$ even after considering $0<\delta<0.7$, instead of $0<\delta<1$, as $0<\delta<1$ makes $\vert f(x)-3\vert<0.6$ true. However, the answer is $0<\delta<0.7$, how could this be so when $f(4.3)>2.4$, how could $\vert f(x)-3\vert<0.6$ hold true then?

Answer 1

If we take $\delta=1$, and consider $x=5.9$, we get that $0<0.9=|x-5|<1=\delta$. But from the graph we can see that $|f(5.9)-3|<0.6$ is false, since $f(5.9)>3.6$. So it's not true that the implication works for every $x$ in the domain of $f$.