When the graph of y=2^x is reflected in the x-axis, and then translated 5 units left and 1 unit down, the equation representing the new graph is:

a) y=2^(-x+5)-1
b) y=2^(x+5)-1
c) y=2^(x-5)+1
d) y=2^(x+5)-1

translated left means subtract 5. one unit down means add one to y, or add one to y, or subtract from the other side.

Well, when you reflect something in the x-axis, it's like flipping it upside down. So the positive values become negative, and the negative values become positive.

Now, when you translate something 5 units left and 1 unit down, you're basically shifting the entire graph to the left and downward.

So, to reflect the graph in the x-axis, we change the sign in front of the x in the equation. This gives us y = 2^(-x).

Then, to translate the graph 5 units left, we subtract 5 from x. This gives us y = 2^(-x+5).

Finally, to translate the graph 1 unit down, we subtract 1 from y. This gives us the equation y = 2^(-x+5)-1.

Therefore, the correct answer is (a) y = 2^(-x+5)-1.

To find the equation representing the new graph, we need to follow the given transformations step by step.

1. Reflecting the graph in the x-axis: This transformation changes the sign of y. So, the original equation y=2^x becomes y=-2^x.

2. Translating 5 units left: This horizontal translation will affect the exponent of x. We need to replace x with (x+5) to shift the graph 5 units to the left. So, the equation becomes y=-2^(x+5).

3. Translating 1 unit down: This vertical translation will affect the constant term. We subtract 1 from the new equation to shift the graph 1 unit down. So, the equation becomes y=-2^(x+5)-1.

Therefore, the equation representing the new graph is y=-2^(x+5)-1.

None of the given options matches the correct equation, so the correct answer is not listed.

To find the equation of the new graph, we need to consider the transformations applied to the original graph of y = 2^x.

First, when the graph is reflected in the x-axis, the sign of the exponent changes from positive to negative. So, the equation becomes y = 2^(-x).

Next, the graph is translated 5 units to the left. This means that every x-coordinate in the equation should be replaced by (x + 5). So, the equation becomes y = 2^(-x-5).

Lastly, the graph is also translated 1 unit down. This means that every y-coordinate in the equation should be decreased by 1. So, the equation becomes y = 2^(-x-5) - 1.

Therefore, the correct equation representing the new graph is y = 2^(-x-5) - 1.

Hence, the answer is a) y = 2^(-x+5) - 1.