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 2x^{2} grows twice as fast as x^{2}, so its graph is tall and skinny. On the other hand, the parabola for the function ( ^{1}/_{2} )x^{2} grows only half as fast, so its graph is short and fat.".
How come the parabola for 2x^{2}is tall and skinny? Aren't both the parabola for 2x^{2} and ( ^{1}/_{2} )x^{2} of the same "height"? (Are they both go to infinity?) So why is the parabola for 2x^{2} tall and the parabola for( ^{1}/_{2} )x^{2} short?