How are the graphs $f (x) = x^{2}$ $f(x)=x^2$ and $g (x) = {(0.2 x)}^{2}$ $g(x)=(0.2x)^2$ related?

Question

1771 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-13T00:37:07

$g (x) = 0.04 f (x)$ $g(x) =0.04 f(x)$

So g(x) is a scaled-down version of f(x)

If $f (x) = x^{2}$ $f(x) = x^2$ , then $x = \pm \sqrt{f (x)}$ $x = pm sqrt (f(x))$ .

It follows that:

$g (x) = {(0.2 x)}^{2} = {(0.2 (\pm \sqrt{f (x)}))}^{2}$ $g(x)=(0.2x)^2 =(0.2(pm sqrt (f(x))))^2$

$= 0.04 f (x)$ $=0.04 f(x)$

It would, of course, be a lot simpler to expand the original expressions:

$f (x) = x^{2}$ $f(x) = x^2$ ,

and

$g (x) = {(0.2 x)}^{2} = 0.04 x^{2}$ $g(x)=(0.2x)^2 = 0.04 x^2$

$\Rightarrow g (x) = 0.04 f (x)$ $implies g(x) =0.04 f(x)$

How are the graphs f(x)=x^2f(x)=x2f(x)=x^2 and g(x)=(0.2x)^2g(x)=(0.2x)2g(x)=(0.2x)^2 related?