Question

which best describes the graph of \\(f(x) = \log_2(x + 3) + 2\\) as a transformation of the graph of \\(g(x) = \log_2 x\\)?

• a translation 3 units right and 2 units up
• a translation 3 units left and 2 units up
• a translation 3 units up and 2 units right
• a translation 3 units up and 2 units left

Explanation:

Identify the horizontal translation

Using the Logarithmic Function Transformations knowledge point

$$
LATEXBLOCK0
$$

Identify the vertical translation

Using the Logarithmic Function Transformations knowledge point

$$
LATEXBLOCK1
$$

Combine the transformations

Using the Logarithmic Function Transformations knowledge point

$$ \text{The graph of } f(x) \text{ is a translation of } g(x) \text{ by } 3 \text{ units left and } 2 \text{ units up.} $$

Answer:

• a translation 3 units right and 2 units up
• a translation 3 units left and 2 units up (Correct answer)
• a translation 3 units up and 2 units right
• a translation 3 units up and 2 units left