Question

below is the graph of $y = 2^x$. translate it to become the graph of $y = 2^{x - 4}+3$.

Explanation:

Step1: Horizontal translation rule

For a function \(y = f(x)\), the graph of \(y=f(x - h)\) is the graph of \(y = f(x)\) shifted \(h\) units to the right. Here, \(f(x)=2^{x}\) and \(y = 2^{x-4}\), so \(h = 4\).

Step2: Vertical translation rule

For a function \(y = f(x)\), the graph of \(y=f(x)+k\) is the graph of \(y = f(x)\) shifted \(k\) units up. Here, \(y = 2^{x - 4}+3\) and \(k=3\).

Answer:

Translate the graph of \(y = 2^{x}\) \(4\) units to the right and \(3\) units up.