Step-by-step explanation:
TRANSFORMATIONS:
Vertical shifts: [tex]f(x)\pm n[/tex] Shifts up/down n units
Horizontal shifts: [tex]f(x\pm n)[/tex] Shifts left/right n units
Reflection: [tex]-f(x)[/tex] Reflection over x-axis
Reflection: [tex]f(-x)[/tex] Reflection over y-axis
Dilation: [tex]f(nx)[/tex]
Dilation of x-coordinate n > 1 graph narrows; n < 1 graph widens
Dilation: [tex]nf(x)[/tex]
Dilation of y-coordinate n > 1 graph narrows; n < 1 graph widens.
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We have:
[tex]f(x)=2^x[/tex]
[tex]g(x)=\dfrac{1}{3}\cdot2^{x-7}=\dfrac{1}{3}f(x-7)[/tex]
Dilation of y-coordinate (graph widens) and Shifts right 7 units.
look at the picture.
