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The base function is given as y=0.3^x and we are asked to describe the transformation of the graph by y=-0.3^(-x+5)
If f(x) is the base function and af(b(x-h))+k is the transformed function we have the following:
a: if a<0 the graph is reflected over the horizontal axis. If |a|>1 there is a vertical stretch of factor a, and if |a|<1 there is a vertical compression of factor a.
b: If b<0 there is a reflection over the vertical axis. If |b|<1 there is a horizontal stretch of factor b and if |b|>1 there is a horizontal compression of factor b. If f(x) is periodic, b affects the period.
h: h performs a horizontal translation of h units
k: k performs a vertical translation of k units.
So for the given function we reflect over the x-axis and compress by a factor 0.3; then we reflect over the y axis; followed by a translation of 5 units to the right. (Write as -.3^(-(x-5)) so a=-.3,b=-1,h=5,and k=0)
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