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How are the graphs #f(x)=x^2# and #g(x)=4(x-3)^2# related?

Answer 1

#g(x)# is shifted 3 units right and stretched vertically by a factor of 4 (#4*y#). That means #(1,1)# becomes #(1,4)# etc. as the graph shows.

#f(x)=x^2#

graph{x^2 [-10, 10, -5, 5]}

#g(x)=4(x-3)^2#

graph{4(x-3)^2 [-10, 10, -5, 5]}

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Answer 2

Theodore Amidon

The graphs of ( f(x) = x^2 ) and ( g(x) = 4(x-3)^2 ) are related by a vertical stretch and a translation. Specifically, the graph of ( g(x) ) is obtained by stretching the graph of ( f(x) ) vertically by a factor of 4 and then translating it 3 units to the right.

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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.