select the correct answer from each drop - down menu. consider the function f(x)=3x + 1 and the graph of the…

select the correct answer from each drop - down menu. consider the function f(x)=3x + 1 and the graph of the function g(x) shown below. the graph g(x) is the graph of f(x) translated units, and g(x)=

select the correct answer from each drop - down menu. consider the function f(x)=3x + 1 and the graph of the function g(x) shown below. the graph g(x) is the graph of f(x) translated units, and g(x)=

Answer

Explanation:

Step1: Find the y - intercept of (f(x))

For (f(x)=3x + 1), when (x = 0), (y=f(0)=3\times0 + 1=1).

Step2: Find the y - intercept of (g(x))

From the graph of (g(x)), when (x = 0), (y=-5).

Step3: Determine the vertical translation

The change in the y - intercept from (f(x)) to (g(x)) is (1-(-5)=6). So the graph of (g(x)) is the graph of (f(x)) translated 6 units down.

Step4: Write the equation of (g(x))

If (f(x)=3x + 1) is translated 6 units down, then (g(x)=3x+1 - 6=3x - 5).

Answer:

The graph (g(x)) is the graph of (f(x)) translated 6 units down, and (g(x)=3x - 5)