is taller than if you plot it only on a bounded segment . Also, for each b > 0, the "girth" of at height b, i.e., where and , is smaller than the analogously defined girth of at height b.
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?