Answer
1. $f(x)=x^2, f(2x)=(2x)^2=4x^2=4f(x)$ end prove.
2. Shrinking the graph horizontally would give $f(cx)=c^2x^2=c^2f(x)$ where c is the factor.
This has the same effect as stretching it vertically by a factor of $c^2$.
3. For $g(x)=e^x$, a horizontal left shift of $b$ would be $g(x+b)=e^{x+b}=e^be^x=e^bg(x)$ which would be the same as stretching it vertically by a factor of $e^b$.
4. For $h(x)=lnx$, a horizontal shrinking by a factor $c$ would give $h(cx)=ln(cx)=lnc+lnx=lnc+h(x)$ which would be the same as a vertical shift of $lnc$, end prove.
Work Step by Step
see above.
