Question

what is the transformation that occurs to the equation y=2^x if the equation changes to y=-2^X^+^1 -1?
1.the transformation moves the graph 1 unit to the left and 1 unit down.
2.transformation moves graph 1 unit to the left,1 unit down and reflects that graph across the y-axis.
3. transformation moves the graph 1 unit to the left,1 unit down and reflects that graph across the x-axis.
4. transformation moves the graph 1 unit to the right,1 unit down and reflects that graph across the x-axis.

Answer 1

think of y = 2^x as y = f(x)

changing the sign of f(x) to -f(x) is a reflection across the x axis.
adding to f(x), such as f(x) + 1, moves the graph up and down (you figure out which)
adding to the argument of f(x), such as f(x+1), moves the graph right and left (again, you figure out which)

these transformations can be applied in any combination you like.

Answer 2

btw, I can't tell what y = -2^x^+^1 -1 is supposed to be...