Question

if you are given the graph of (g(x) = log_2 x), how could you graph (f(x) = log_2 x + 5)?

translate each point of the graph of (g(x)) 5 units up.
translate each point of the graph of (g(x)) 5 units down.
translate each point of the graph of (g(x)) 5 units left.
translate each point of the graph of (g(x)) 5 units right.

Explanation:

Identify the relationship between the functions

$$ f(x) = g(x) + 5 $$

Apply the vertical translation rule

$$ y = g(x) + c \quad (c > 0) \implies \text{Shift up by } c \text{ units} $$

Determine the specific transformation

$$ c = 5 \implies \text{Translate each point of the graph of } g(x) \text{ 5 units up.} $$

Answer:

• Translate each point of the graph of g(x) 5 units up. (Correct answer)
• Translate each point of the graph of g(x) 5 units down.
• Translate each point of the graph of g(x) 5 units left.
• Translate each point of the graph of g(x) 5 units right.