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How do you find the domain and range of #g(x) = 2(1/2)^(2x) +3#?

Answer 1

#"Domain":(-∞,∞)#
#"Range":(3,∞)#

The Domain for almost any exponential function is #(-∞,∞)#.

To assist with the Range, determine the asymptote.

The asymptote is #y=3#.

The exponential function will always approach, but never touch, the asymptote—graphing calculators will eventually round it off, though.

Since the function is decreasing from infinity, the range is #(3,∞)#

This graph is available:

graph{[-10, 10, -5, 5]} = 2*(1/2)^(2x)+3

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Answer 2

Eva Adamson

Domain: All real numbers Range: ( (3, +\infty) )

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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.