Instructions: For the function given, determine the direction and amount of vertical shift from the function y=(2)x𝑦=(2)𝑥.y=6(2)x−3−5

1. ### Break Down the Problem

To determine the direction and amount of vertical shift for the function $y = 6(2)^x - 3 - 5$, we first rewrite the equation in a standard format and analyze the transformations involved.

2. ### Relevant Concepts

The general form of a vertical shift in an exponential function $y = a(2)^x + k$ is represented by the term $k$:

• If $k > 0$, the graph shifts vertically upwards by $k$ units.
• If $k < 0$, the graph shifts vertically downwards by $|k|$ units.

3. ### Analysis and Detail

We can rewrite the given function as follows: $y = 6(2)^x - (3 + 5)$ This simplifies to: $y = 6(2)^x - 8$

Here, the effective vertical shift $k = -8$. Since $k < 0$, this indicates a vertical shift downwards.

4. ### Verify and Summarize

We conclude that the graph has shifted vertically down by 8 units. There are no other transformations affecting the direction of the vertical shift.

Final Answer

The function $y = 6(2)^x - 3 - 5$ is shifted vertically down by 8 units.