soevse
13.09.2021 •
Mathematics
The triangle on the right is a scaled copy of the triangle on the left. Identify the scale
factor. Express your answer as a whole number or fraction in simplest form.
20
20/3
A A
20/3
20
Solved
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Ответ:
The transformation from f(x) to g(x) using
g(x)=a*f(x-h)+k
will stretch f(x) by a scale factor of a (>0), translates to the right by h, and translates upwards of k.
Similarly, the transformation from f(x) to g(x) using
g(x)=-a*f(x-h)+k
will stretch f(x) by a scale factor of a (>0) AND reflects over the x-axis, translates to the right by h, and finally translates upwards of k.
For the given problem,
f(x)=log_3(x)
a=-2 (dilates with scale factor of 2, AND with reflection over the x-axis)
h=0 (no horizontal translation)
k=3 (translates UPwards by 3 units)
Put into the above formula,
g(x)=-2f(x)+3=-2log_3(x)+3.
Note: in case you are not familiar with it, _ means subscript, and ^ means superscript, applicable to some text processing software.