Let's analyze the given functions and understand how their graphs are related.
Given functions:
[tex]\[ f(x) = 2x \][/tex]
[tex]\[ g(x) = 2x + 3 \][/tex]
To determine the relationship between the graphs of [tex]\( f \)[/tex] and [tex]\( g \)[/tex], we can rewrite [tex]\( g(x) \)[/tex] in terms of [tex]\( f(x) \)[/tex]. Notice that:
[tex]\[ g(x) = 2x + 3 \][/tex]
By substituting [tex]\( f(x) \)[/tex] into the equation for [tex]\( g(x) \)[/tex], we get:
[tex]\[ g(x) = f(x) + 3 \][/tex]
This equation shows that [tex]\( g(x) \)[/tex] is equal to [tex]\( f(x) \)[/tex] plus a constant value of 3. This constant addition of 3 means that for any value of [tex]\( x \)[/tex], the value of [tex]\( g(x) \)[/tex] is always 3 units higher than the value of [tex]\( f(x) \)[/tex].
Graphically, this translates to a vertical shift of the graph of [tex]\( f(x) \)[/tex] upward by 3 units to get the graph of [tex]\( g(x) \)[/tex]. Therefore, the correct statement that describes the graph of [tex]\( g(x) \)[/tex] compared to the graph of [tex]\( f(x) \)[/tex] is:
B. The graph of [tex]\( g \)[/tex] is 3 units above the graph of [tex]\( f \)[/tex].
So, the correct answer is:
[tex]\[ \boxed{B} \][/tex]
