Question

select the correct answer.

consider the function \\(f(x) = 2^x\\) and function \\(g\\).

\\(g(x) = f(x) + 6\\)

how will the graph of function \\(g\\) differ from the graph of function \\(f\\)?

• the graph of function \\(g\\) is the graph of function \\(f\\) shifted 6 units down.
• the graph of function \\(g\\) is the graph of function \\(f\\) shifted 6 units to the left.
• the graph of function \\(g\\) is the graph of function \\(f\\) shifted 6 units up.

Explanation:

Identify the transformation rule

$$ g(x) = f(x) + k $$

Apply the vertical shift value

$$
LATEXBLOCK0
$$

Determine the direction of the shift

$$ k > 0 \implies \text{Shifted 6 units up} $$

Answer:

• The graph of function g is the graph of function f shifted 6 units down.
• The graph of function g is the graph of function f shifted 6 units to the left.
• The graph of function g is the graph of function f shifted 6 units up. (Correct answer)
• The graph of function g is the graph of function f shifted 6 units to the right.