Question

given the function f(x) = 2x + 3, describe the transformation represented by g(x) = f(x − 5). horizontal translation 5 units to the left horizontal translation 5 units to the right vertical translation 5 units downward vertical translation 5 units upward

Explanation:

For a function \(y = f(x)\), the transformation \(y = f(x - h)\) (where \(h>0\)) represents a horizontal translation. The rule is that if we have \(y = f(x - h)\), the graph of the function is shifted \(h\) units to the right. In the given case, \(g(x)=f(x - 5)\) (comparing with \(y = f(x - h)\), here \(h = 5\)). There is no addition or subtraction outside the function \(f\) (like \(f(x)+k\) or \(f(x)-k\) which would be vertical translations).

Answer:

Horizontal translation 5 units to the right.