Question

what kind of transformation converts the graph of f(x) = -5x - 1 into the graph of g(x) = -5x - 3? translation 2 units left translation 2 units up translation 2 units right translation 2 units down

Explanation:

Step1: Recall the transformation rule for vertical translation

For a function \(y = f(x)\), if \(y=f(x)+k\), when \(k>0\) the graph is translated \(k\) units up and when \(k < 0\) the graph is translated \(|k|\) units down.
We can rewrite \(g(x)\) in terms of \(f(x)\). Given \(f(x)=-5x - 1\) and \(g(x)=-5x - 3\), we can express \(g(x)\) as \(g(x)=f(x)-2\).

Answer:

translation 2 units down