Sketch y= -(1/4) (2)^(x-4)+5

I know that the basic equation is y=2^x

so is the graph translated 4 units right, vertically stretched by a factor of (1/4), reflected on the x-axis and translated up 5?

Yes, you are correct. The given equation is a transformation of the basic equation y = 2^x. Let's break down the transformations step by step:

1. Translation 4 units to the right: The original equation y = 2^x is shifted horizontally to the right by 4 units. This means that for each x-value, you need to substitute x-4 in the equation. The equation becomes y = 2^(x-4).

2. Vertical stretching by a factor of (1/4): The original equation y = 2^x is vertically stretched by a factor of 1/4. This means that each y-value is multiplied by (1/4). The equation becomes y = (1/4) * 2^(x-4).

3. Reflection on the x-axis: The original equation y = 2^x represents an exponential growth, where the y-values increase as x increases. However, in the given equation y = (1/4) * 2^(x-4), the negative sign in front of the whole equation reflects it across the x-axis. This reflects the graph so that the y-values now decrease as x increases.

4. Translation up 5 units: After applying the above transformations, the graph is then shifted vertically upwards by 5 units. This means that each y-value is increased by 5. The equation becomes y = (1/4) * 2^(x-4) + 5.

By following these transformations, you correctly described the graph of the given equation.