Which statement describes the graph of function g?

f(x) = 2x
g(x) = 2x + 3

A.
The graph of g is 3 units above the graph of f.
B.
The graph of g is 3 units below the graph of f.
C.
The graph of g is 3 units to the right of the graph of f.
D.
The graph of g is 3 units to the left of the graph of f.

1 answer

To determine how the graph of \( g(x) = 2x + 3 \) compares to the graph of \( f(x) = 2x \), consider the effect of the "+ 3" in \( g(x) \).

The function \( g(x) = 2x + 3 \) can be thought of as adding 3 to the output of \( f(x) = 2x \). This means that for any given value of \( x \),

\[ g(x) = f(x) + 3 \]

Therefore, at each point \( x \), the value of \( g(x) \) is exactly 3 units higher than the value of \( f(x) \).

Graphically, this means that the graph of \( g(x) = 2x + 3 \) is a vertical shift of the graph of \( f(x) = 2x \) by 3 units upward.

So, the correct description is:

**A. The graph of g is 3 units above the graph of f.**