To shift the graph of h(x) = -2^x+3 left 7 units and down 5 units, we need to modify the equation as follows:
k(x) = -2^(x+7) - 5
Here's how we arrived at this equation:
To shift the graph left 7 units, we need to subtract 7 from x, so we have:
h(x+7) = -2^x+3
To shift the graph down 5 units, we need to subtract 5 from the entire function, so we have:
h(x+7) - 5 = -2^x+3 - 5
Simplifying the right-hand side of the equation, we get:
h(x+7) - 5 = -2^x-2
Finally, substituting h(x+7) with its original expression, we get:
k(x) = -2^(x+7) - 5
Therefore, the function k(x) that shows the graph of h(x)=-2^x+3 shifted left 7 units and down 5 units is k(x) = -2^(x+7) - 5.