Question

below is the graph of $y=3^{x}$.
translate it to become the graph of $y=3^{x-2}+1$.
try one last time

Explanation:

Step1: Identify horizontal translation

For $y=3^{x-h}$, shift right by $h$. Here $h=2$, so shift right 2 units.

Step2: Identify vertical translation

For $y=3^{x-2}+k$, shift up by $k$. Here $k=1$, so shift up 1 unit.

Step3: Apply translations to key points

• Original key point of $y=3^x$: $(0,1)$. After shifting right 2, up 1: $(0+2, 1+1)=(2,2)$.
• Original asymptote: $y=0$. After vertical shift, new asymptote: $y=1$.
• Another original point: $(1,3)$. After shifts: $(1+2, 3+1)=(3,4)$.

Answer:

Translate the entire graph of $y=3^x$ 2 units to the right and 1 unit upward. The new graph will have a horizontal asymptote at $y=1$, pass through $(2,2)$ and $(3,4)$, and maintain the same exponential growth shape as the original graph.