# Math Help - graph of functions

1. ## graph of functions

Function Transformations / Translations: Additional Rules
It mentions "The parabola for 2x2 grows twice as fast as x2, so its graph is tall and skinny. On the other hand, the parabola for the function ( 1/2 )x2 grows only half as fast, so its graph is short and fat.".

How come the parabola for 2x2is tall and skinny? Aren't both the parabola for 2x2 and ( 1/2 )x2 of the same "height"? (Are they both go to infinity?) So why is the parabola for 2x2 tall and the parabola for( 1/2 )x2 short?

2. ## Re: graph of functions

$2x^2$ is taller than $(1/2)x^2$ if you plot it only on a bounded segment $[-a, a]$. Also, for each b > 0, the "girth" of $2x^2$ at height b, i.e., $|x_2(b)-x_1(b)|$ where $x_1(b)\ne x_2(b)$ and $2(x_1(b))^2=2(x_2(b))^2=b$, is smaller than the analogously defined girth of $(1/2)x^2$ at height b.