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luisejr77

Answer: 1. [tex]g(x)[/tex] is translated 7 units down from [tex]f(x)[/tex]

Step-by-step explanation:

The missing statements are:

1. [tex]g(x)[/tex] is translated 7 units down from  [tex]f(x)[/tex]

2. [tex]g(x)[/tex] is translated 7 units left from  [tex]f(x)[/tex]

3. [tex]g(x)[/tex] is translated 7 units up from  [tex]f(x)[/tex]

4. [tex]g(x)[/tex] is translated 7 units right from  [tex]f(x)[/tex]

Below are shown some transformations for a function  [tex]f(x)[/tex]:

If [tex]f(x)+k[/tex], the function is shifted up "k" units.

If [tex]f(x)-k[/tex], the function is shifted down "k" units.

If [tex]f(x+k)[/tex], the function is shifted left "k" units.

If [tex]f(x-k)[/tex], the function is shifted right "k" units.

Then, in this case, given the function  [tex]f(x)[/tex]:

[tex]f(x) = 5^x[/tex]

And given the function [tex]g(x)[/tex]:

[tex]g(x) = 5^x-7[/tex]

You can identify the transformation:

[tex]f(x)-k[/tex]

Therefore, based on the transformations explained before, you can conclude that the graph of the function [tex]g(x)[/tex] is translated 7 units down from the graph of the  function [tex]f(x)[/tex].

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