Question

given the function f(x) = x + 1, describe the type of transformation represented by g(x) = f(x) + 3. vertical translation 3 units upward vertical translation 3 units downward horizontal translation 3 units to the left horizontal translation 3 units to the right

Explanation:

Step1: Recall the rule for vertical translation

For a function \(y = f(x)\), the transformation \(y=f(x)+k\) is a vertical translation. If \(k>0\), it is a translation \(k\) units upward. If \(k < 0\), it is a translation \(|k|\) units downward.

Step2: Analyze \(g(x)=f(x)+3\)

Here, \(k = 3>0\). So, for the function \(g(x)=f(x)+3\) (where \(f(x)=x + 1\)), according to the rule \(y=f(x)+k\) with \(k = 3\), the transformation is a vertical translation.

Answer:

Vertical translation 3 units upward