F(x)= 7x + 9 g(x) = 7x - 4 the graph of g(x) is obtained by shifting down the graph of f(x)

Answser: the graph of g(x0 is obtained by shifting down 13 units. the graph of f(x).

Explanation:

It is a rule that when you add a constant to a function the graph is shifted upward the number of units that the constant represent, when the constant is posivite, or downward the number of units that the constant represent, whtn the constant is negative.

So, the graph of any function h(x) + k, being k a constant, will be the graph of h(x) shifted k units upward (if k iis positive) or downward (if k is negative).

Then, you have to find how many units you have to add to f(x) = 7x + 9 to become the function g(x) = 7x - 4. That is, find k in:

7x + 9 + k = 7x - 4

⇒ k = - 4 - 9 = - 13.

So, you have that the graph of g(x) = 7x - 4  is found when you add - 13 to add  - 13 to the graph of f(x) = 7x + 9.

Which, as explained before is shifting 13 units down.