I'm currently trying to get myself through Khan Academy, and I am completely loss in function transformation.
Twice I have been essentially guessing at the what to do in terms of these transformation because I can't understand the concept of maginitude less than 1. I have no idea what it means, and it is in several exercises without explanation.
Here is a link to the section.
CASE $1$: Magnitude Greater than $0$ but Less than $1$
A magnitude less than $1$ means a function with the $a$ term $0<a<1$, where $f(x)=ax^2+bc+c$. This is for quadratic functions.
Take an example of the function $x^2$. To vertically shrink it by a factor of $2$ would mean to multiply the $a$ term by $1/2$.
Therefore, the $a$ term, or the "magnitude", would now be $1/2$, and the function would be $f(x)=1/2x^2$, a function with a magnitude less than $1$ but greater than $0$.
CASE $2$: Magnitude Less than $0$
The function $f(x)=x^2$, if you make the magnitude of the function $-1$, the function would be $f(x)=-x^2$. This means reflecting the original function over the $x$ axis.
Here is a graph which displays $f(x)=x^2$(RED), $g(x)=1/2x^2$(GREEN), and $h(x)=-x^2$ (YELLOW)