Respuesta :
The lines have the same slope, so they'll be moving the same exact way except they have different y-intercepts.
Answer:
The graph of g(x) is a translation of f(x) 2 units down.
Step-by-step explanation:
Given : Graph of [tex]g(x)=3x-2[/tex] and [tex]f(x)=3x[/tex]
To find : How does the graph of g(x) compare to the graph of f(x)?
Solution :
[tex]f(x)=3x[/tex]
[tex]g(x)=3x-2[/tex]
We can re-write the g(x) as
[tex]g(x)=f(x)-2[/tex]
The translation of a function is defined as
[tex]g(x)=f(x)+b[/tex]
where, b is vertical shift.
If b>0, then f(x) shifts b units up and if b<0, then f(x) shifts b units down.
On comparing, b=-2<0.
So, the graph of f(x) shifts 2 units down.
The graph of g(x) is a translation of f(x) 2 units down.