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How is the graph of #h(x)=2-x^2# related to the graph of #f(x)=x^2#?

Answer 1

#h(x)=2-x^2# is the graph of #f(x)=x^2# reflected in the X-axis and then shifted up #2# units.

In the event that #f(x)=x^2#, then #g(x)=-x^2# represents #f(x)#'s reflection in the X-axis, and #h(x)=2-x^2# represents (g(x)# shifted up #2# units.

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Answer 2

Kennedy Adams

The graph of ( h(x) = 2 - x^2 ) is related to the graph of ( f(x) = x^2 ) by a vertical shift of 2 units downward.

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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.