Answered

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Which statement describes the graph of function [tex]g[/tex]?

[tex]\[ \begin{array}{l}
f(x)=2x \\
g(x)=2x+3
\end{array} \][/tex]

A. The graph of [tex]g[/tex] is 3 units below the graph of [tex]f[/tex].

B. The graph of [tex]g[/tex] is 3 units above the graph of [tex]f[/tex].

C. The graph of [tex]g[/tex] is 3 units to the left of the graph of [tex]f[/tex].

D. The graph of [tex]g[/tex] is 3 units to the right of the graph of [tex]f[/tex].

Sagot :

GinnyAnswer
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]
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