Questions: Below is the graph of y=(1/2)^x Translate it to become the graph of y=(1/2)^(x+3)+1

Transcript text: Below is the graph of $y=\left(\frac{1}{2}\right)^{x}$ Translate it to become the graph of $y=\left(\frac{1}{2}\right)^{x+3}+1$

Solution

Solution Steps

Step 1: Horizontal Shift

The graph of $y = \left(\frac{1}{2}\right)^{x+3}$ is a horizontal shift of the graph of $y = \left(\frac{1}{2}\right)^x$ to the left by 3 units.

Step 2: Vertical Shift

The graph of $y = \left(\frac{1}{2}\right)^{x+3} + 1$ is a vertical shift of the graph of $y = \left(\frac{1}{2}\right)^{x+3}$ upwards by 1 unit.

Step 3: Combining the Transformations

To obtain the graph of $y = \left(\frac{1}{2}\right)^{x+3} + 1$ from the graph of $y = \left(\frac{1}{2}\right)^x$, we shift the original graph 3 units to the left and 1 unit upwards.

Final Answer

The graph of $y=\left(\frac{1}{2}\right)^{x+3}+1$ is obtained by shifting the graph of $y=\left(\frac{1}{2}\right)^{x}$ three units to the left and one unit up. \$ \boxed{ \text{Shift left 3, up 1} } \$

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