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If G(x)=1/x were shifted 4 units to the left and 4 units up, what would the new equation be?

Answer 1

#f(x) = 1/(x+4)+4#

Given:

#g(x) = 1/x#

graph{1/x [-10, 10, -5, 5]}

If we want our new function to be like #g(x)# but shifted left #4# units, then we need to put #x+4# in place of #x#. That way, when you put #-4# into the new function then the result is the same as putting #0# into the old - i.e. an undefined result since that's where #1/x# has its vertical asymptote.

To move our new function up #4# units, simply add #4#.

So our transformed function is:

#f(x) = 1/(x+4)+4#

graph{1/(x+4)+4 [-12.125, 7.875, -2.28, 7.72]}

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Answer 2

Serenity Johnson

The new equation would be ( G(x) = \frac{1}{x+4} + 4 ).

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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.