Spivak Calculus, Ch. 4 Graphs, Problem 19v: How to interpret graph in solution manual?

In my original answer I read the problem description incorrectly. We must replace all digits in the decimal expansion of $x$ which come after the first $7$.

For example, between $x=0.7$ and $x=0.8=0.7\bar{9}$, $f(x)=0.7$. This is the large interval we see in the solution manual solution.

Note that for $x=0.7=0.6\bar{9}$, $f(0.7)$ does not equal 0.7 apparently because $0.6\bar{9}$ is used.

Another example is the interval between $x=0.697$ and $x=0.698$. $f(x)=0.697$ in this interval except at $x=0.697=0.696\bar{9}$.

In the interval between $x=0.6967$ and $x=0.6968$ we have $f(x)=0.6967$ except at $x=0.6967=0.696\bar{9}$

Function $f$ seems to be composed of infinite intervals like this, mixed with points on the line $y=x$ for numbers with no sevens in them.

Consider $x=1.7$. Again we have a larger interval between $x=1.7$ and $x=1.8$ in which $f(x)=1.7$ except at $x=1.7$.