Question 74437
If you reflect the equation {{{y=7^x}}} across the y=0 line you get this graph {{{y=-7^x}}} since each y value is now the opposite. If we're doing this across the y=-1 line, we get the same thing, but it's shifted. Since the graph {{{y=7^x}}} hits the y-axis at (0,1) it is 2 units away from the line y=-1. So the intercept of the reflected graph is 2 units away from the line y=-1 (which is (0,-3). So the equation is {{{y=-7^x-2}}} since the general equation of a exponential function is {{{y=ab^x+c}}} where c+1 is the intercept  (ie the intercept is (0,c+1). Since the entire thing is negated it looks like
{{{y=-(ab^x+c)}}} where c-1 is the intercept.

{{{graph( 300, 200, -3, 2, -5, 5, 7^x, -1, -7^x-2) }}}Equations {{{y=7^x}}}(red) ,{{{y=-7^x-2}}}(dark blue), and the line of reflection y=-1 (green).