Respuesta :
f(x) + n - translate the graph n units up
f(x) - n - translate the graph n units down
f(x + n) - translate the graph n units left
f(x - n) - translate the graph n units right
nf(x) - dilation of the graph along the Oy axis and the scale n
f(nx) - dilation of the graph along the Ox axis and the scale 1/n
-f(x) - symmetry of the graph with respect to the Ox axis
f(-x) - symmetry of the graph with respect to the Oy axis
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[tex]f(x)=-3\cdot2^{x-1}-1\\\\g(x)=2^x\\\\3g(x)=3\cdot2^x-\text{dilatation by a scale of 3}\\\\-3g(x)=-3\cdot2^x-\text{symmetry of the graph with respect to the Ox axis}\\\\-3g(x-1)=-3\cdot2^{x-1}-\text{translate the graph 1 unit right}\\\\-3g(x-1)-1=f(x)=-3\cdot2^{x-1}-1-\text{translate the graph 1 unit down}[/tex]
[tex]f(x)=-\dfrac{1}{4}\cdot2^{x+1}-1\\\\g(x)=2^x\\\\\dfrac{1}{4}g(x)=\dfrac{1}{4}\cdot2^x-\text{dilatation by a scale of}\ \dfrac{1}{4}\\\\-\dfrac{1}{4}g(x)=-\dfrac{1}{4}\cdot2^x-\text{symmetry of the graph with respect to the Ox axis}\\\\-\dfrac{1}{4}g(x+1)=-\dfrac{1}{4}\cdot2^{x+1}-\text{translate the graph 1 unit left}\\\\-\dfrac{1}{4}g(x+1)-1=f(x)=-\dfrac{1}{4}\cdot2^{x+1}-1-\text{translate the graph 1 unit down}[/tex]