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Which function k(x) shows the graph of h(x)=-2^x+3 shifted left 7 units and down 5 units?

User Kronos
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1 Answer

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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.

User Gndps
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