Answer:
[tex]g(x)= 3x-2[/tex], graph shifted 2 units down.
Step-by-step explanation:
[tex]g(x)= 3x-2[/tex]
g(x) = 3x is a parent function.
When we compare the graph of parent function g(x)= 3x with [tex]g(x)= 3x-2[/tex], negative 2 is added at the end
f(x)---> f(x) + a , the graph will be shifted 'a' units up
f(x)-> f(x) -a , the graph will be shifted 'a' units down
[tex]g(x)= 3x-2[/tex], In this g(x) we have -2 at the end.
So the graph will be shifted 2 units down.
The graph of 3x - 2 is a vertical translation by 2 units down of the function f(x) = 3x
According to the question, we are given the parent function f(x) = 3x, we need to determine the relationship between the parent function and g(x) = 3x - 2
If the function f(x) translate by k units downwards, the resutlting function will be expressed as h(x) - k.
Hence if h(x) = 3x translate by 2 units downwards, the resulting function will be expressed as 3x - 2.
The graph of 3x - 2 is a vertical translation by 2 units down of the function h(x) = 3x
Learn more on translation here: https://brainly.com/question/12861087
