How do you find the range of #f(x)=3^(x+9)+4#?

Answer 1

The range is #x in (4;+oo)#

The exponential fonction #y=a^x# has a range of #(0;+oo)#.

The graph of function #y=3^(x+9)+4# is the graph #y=3^x# moved #9# units to the left and #4# units up. Moving a graph of a function with bounded values up increases the boundaries, so #f(x)# has only values greater than #4#.

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Answer 2

Lily Anderson

To find the range of the function ( f(x) = 3^{x+9} + 4 ), we consider the behavior of the exponential function ( 3^{x+9} ). Since ( 3^{x+9} ) is always positive for any real value of ( x ), adding 4 to it will shift the graph of the exponential function upwards by 4 units. Therefore, the range of the function ( f(x) = 3^{x+9} + 4 ) is all real numbers greater than 4. In interval notation, the range is ( [4, \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.