Question

which translation shifts the graph of $f(x) = 3x + 3$ onto $g(x) = 3x - 3$? 6 units up 6 units down 3 units up 3 units down

Explanation:

Step1: Recall Vertical Translation Rule

For a function \( y = f(x) \), a vertical translation by \( k \) units down is \( y = f(x)-k \), and up is \( y = f(x)+k \).

Step2: Compare \( f(x) \) and \( g(x) \)

Given \( f(x)=3x + 3 \) and \( g(x)=3x-3 \). We can write \( g(x)=f(x)-6 \) (since \( (3x + 3)-6=3x - 3 \)).

Step3: Determine Translation Direction

From the rule of vertical translation, subtracting 6 from \( f(x) \) means shifting the graph of \( f(x) \) 6 units down.

Answer:

6 units down