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

Answer 1

Christian Antunez

#g(x) =0.04 f(x)#

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

If #f(x) = x^2#, then #x = pm sqrt (f(x))#.

It follows that:

#g(x)=(0.2x)^2 =(0.2(pm sqrt (f(x))))^2#

#=0.04 f(x)#

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

#f(x) = x^2#,

and

#g(x)=(0.2x)^2 = 0.04 x^2#

#implies g(x) =0.04 f(x)#

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Answer 2

Xavier Alonso

The graphs of ( f(x) = x^2 ) and ( g(x) = (0.2x)^2 ) are related by a vertical compression by a factor of ( 0.2 ) applied to the graph of ( f(x) = x^2 ). This means that the graph of ( g(x) ) is obtained by compressing the graph of ( f(x) ) vertically, making it narrower. Specifically, every point on the graph of ( f(x) = x^2 ) is vertically compressed towards the x-axis by a factor of ( 0.2 ) to obtain the corresponding points on the graph of ( g(x) = (0.2x)^2 ). Therefore, the graph of ( g(x) ) is narrower than the graph of ( f(x) ) by a factor of ( 0.2 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.