If f(x)=In(x) and g(x) is f(x) translated right one unit and down nine units then reflected over the x axis, what would g(30) be
?
A. -5.9
B. -12.1
C. -12.4
D. -20.1
1 answer:
Answer:
<u>Translations</u>
![f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}](https://tex.z-dn.net/?f=f%28x%2Ba%29%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Btranslated%7D%5C%3Aa%5C%3A%5Ctextsf%7Bunits%20left%7D)
![f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}](https://tex.z-dn.net/?f=f%28x-a%29%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Btranslated%7D%5C%3Aa%5C%3A%5Ctextsf%7Bunits%20right%7D)
![f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}](https://tex.z-dn.net/?f=f%28x%29%2Ba%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Btranslated%7D%5C%3Aa%5C%3A%5Ctextsf%7Bunits%20up%7D)
![f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}](https://tex.z-dn.net/?f=f%28x%29-a%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Btranslated%7D%5C%3Aa%5C%3A%5Ctextsf%7Bunits%20down%7D)
![y=-\:f\:(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}](https://tex.z-dn.net/?f=y%3D-%5C%3Af%5C%3A%28x%29%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Breflected%20in%20the%7D%20%5C%3A%20x%20%5Ctextsf%7B-axis%7D)
![y=f\:(-\:x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}](https://tex.z-dn.net/?f=y%3Df%5C%3A%28-%5C%3Ax%29%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Breflected%20in%20the%7D%20%5C%3A%20y%20%5Ctextsf%7B-axis%7D)
Parent function: ![f\:(x) = \ln(x)](https://tex.z-dn.net/?f=f%5C%3A%28x%29%20%3D%20%5Cln%28x%29)
Translated right 1 unit: ![f\:(x\:-1) = \ln(x - 1)](https://tex.z-dn.net/?f=f%5C%3A%28x%5C%3A-1%29%20%3D%20%5Cln%28x%20-%201%29)
Then translated down 9 units: ![f\:(x\: -1)-9 = \ln(x - 1) - 9](https://tex.z-dn.net/?f=f%5C%3A%28x%5C%3A%20-1%29-9%20%3D%20%5Cln%28x%20-%201%29%20-%209)
The reflected over the x-axis: ![-\:[f\:(x\:-1) - 9] = -\ln(x - 1) + 9](https://tex.z-dn.net/?f=-%5C%3A%5Bf%5C%3A%28x%5C%3A-1%29%20-%209%5D%20%3D%20-%5Cln%28x%20-%201%29%20%2B%209)
Therefore, ![g(x) = -\ln\:(x\:- 1) + 9](https://tex.z-dn.net/?f=g%28x%29%20%3D%20-%5Cln%5C%3A%28x%5C%3A-%201%29%20%2B%209)
⇒ g(30) = - ln(30 - 1) + 9
= -3.36729... + 9
= 5.6 (nearest tenth)
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