Which statement correctly describes the relationship between the graph of f (x) = 2x and the graph of g (x) = f (x) − 4? a. the graph of g (x) is the graph of f (x) translated 4 units up. b. the graph of g (x) is the graph of f (x) translated 4 units right. c. the graph of g (x) is the graph of f (x) translated 4 units left. d. the graph of g (x) is the graph of f (x) translated 4 units down.

D. The graph of g (x) is the graph of f (x) translated 4 units down.

Explanation:

To show a translation left or right, we add or subtract a value to x before the function is applied.  That is not what has happened to this function, therefore this was not a horizontal translation.

To show a translation up or down, we add or subtract a value at the end of a function.  The function g(x) = f(x) - 4 subtracts 4 from the end of the function f(x); this means that the function has been translated down 4 units.

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.