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

Question

asked Apr 8, 2023 197k views

1 Answer

Mylescc · Answer 1 · 2023-04-15T11:14:27+0000

Answer:

Translations

$f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}$

$f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}$

$f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}$

$f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}$

$y=-\:f\:(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}$

$y=f\:(-\:x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}$

Parent function:
$f\:(x) = \ln(x)$

Translated right 1 unit:
$f\:(x\:-1) = \ln(x - 1)$

Then translated down 9 units:
$f\:(x\: -1)-9 = \ln(x - 1) - 9$

The reflected over the x-axis:
$-\:[f\:(x\:-1) - 9] = -\ln(x - 1) + 9$

Therefore,
$g(x) = -\ln\:(x\:- 1) + 9$

⇒ g(30) = - ln(30 - 1) + 9

= -3.36729... + 9

= 5.6 (nearest tenth)