Question

identify the equation that translates \\(y = \ln(x)\\) five units down.

\\(y = \ln(x-5)\\)
\\(y = \ln(x)+5\\)
\\(y = \ln(x+5)\\)
\\(y = \ln(x)-5\\)

Explanation:

⚡ Using what you learned: combining transformations

Step 1: Identify the transformation rule

A vertical translation down by \( k \) units subtracts \( k \) from the entire function:

$$ f(x) \to f(x) - k $$

Step 2: Apply the rule to the function

Given the parent function \( y = \ln(x) \), translating it five units down yields:

$$ y = \ln(x) - 5 $$

Answer:

\( y = \ln(x) - 5 \)