Question

describe the transformation to f(x) that results in g(x).
g(x)=f(x + 5)
f(x) has been translated to the left 5.
f(x) has been translated to the right 5.

Explanation:

Step1: Recall function transformation rules

For a function \(y = f(x)\), the transformation \(y = f(x + h)\) (where \(h>0\)) shifts the graph of \(y = f(x)\) to the left by \(h\) units.

Step2: Apply the rule to \(g(x)=f(x + 5)\)

Here \(h = 5\). According to the rule \(y=f(x+h)\) (left - shift by \(h\) units when \(h>0\)), for \(g(x)=f(x + 5)\), the graph of \(f(x)\) is shifted to the left by \(5\) units.

Answer:

\(f(x)\) has been translated to the left \(5\).