Question

g(x)=f(x)-4
describe the transformation to f(x) that results in g(x).
f(x) has been translated up 4. f(x) has been translated down 4.

Explanation:

Step1: Recall function transformation rules

For a function \( y = f(x)+k \), if \( k>0 \), the graph is translated up \( k \) units; if \( k < 0 \), the graph is translated down \( |k| \) units.

Step2: Analyze \( g(x)=f(x)-4 \)

Here \( k=-4 \). So the graph of \( f(x) \) is translated down 4 units.

Answer:

f(x) has been translated down 4.