Question

what does the transformation f(x) ↦ f(x) - 8 do to the graph of f(x)? translates it 8 units right translates it 8 units down translates it 8 units left translates it 8 units up

Explanation:

Step1: Recall vertical translation rules

For a function transformation of the form \( f(x) \to f(x) + k \), if \( k>0 \), the graph shifts up \( k \) units; if \( k<0 \), the graph shifts down \( |k| \) units.

Step2: Analyze the given transformation

In the transformation \( f(x) \to f(x) - 8 \), we can rewrite it as \( f(x) \to f(x) + (- 8) \). Here, \( k=-8 \), which is negative. So, the graph of \( f(x) \) will shift down by \( | - 8|=8 \) units.

Answer:

translates it 8 units down