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If the graph of the function h defined by #h (x)= 5x^2-1# is translated vertically downward by 4 units, it becomes the graph of a function f. How do you find the expression for f (x)?

Answer 1

Ethan Adkins

Well, It looks to me like you can just subtract 4 from each side...

#h(x) - 4 = 5x^2 - 1 -4#

#f(x) = 5x^2 - 5 = 5(x^2 - 1)#

How does that look?

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Answer 2

Eva Adamson

To find the expression for the function ( f(x) ) resulting from translating the graph of ( h(x) = 5x^2 - 1 ) vertically downward by 4 units, you simply subtract 4 from the function:

[ f(x) = h(x) - 4 = 5x^2 - 1 - 4 = 5x^2 - 5 ]

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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.