7-8 Attributions and Transformations of Natural Logarithms

The graph of $f\left(x\right)=\ln\left(x\right)$  and a graph of a transformation of  $f\left(x\right)$  are shown.  What is the transformed function?

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 What is the domain of the function   $f\left(x\right)=-3\ln\left(x+5\right)-8$  

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Let  $n$  be a nonzero real number. Of the functions  $y=\log_ex+n$  ; $y=\log_e\left(x-n\right)$   ; and $y=n\log_ex$  , which has a different asymptote from the parent function   $y=\log_ex$  ?

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Tags

CCSS.HSF-IF.C.7E

Let  $f\left(x\right)=\ln\left(x\right)$  .  What is the MAXIMUM value over the interval  $1\le x\le e^2$  ?

Let  $f\left(x\right)=\ln\left(x\right)$  .  What is the MINIMUM value over the interval  $1\le x\le e^2$  ?

Tags

CCSS.HSF-IF.C.7E

How does the range of equation  $y=-0.5\ln\left(x-3\right)+6$   change in comparison to the range of the parent function  $y=\ln\left(x\right)$  ?

• The range changed to  $y<-0.5$  

• The range changed to  $y>3$  

• The range changed to  $y<6\$  

• There is no change on the range.

Tags

CCSS.HSF-IF.C.7E

Which transformation maps the graph of  $f\left(x\right)=\ln\left(x\right)$  to the graph of  $g\left(x\right)=\ln\left(x+13\right)$  ?

• a translation of 13 units to the left

• a translation of 13 units down

• a compression by a factor of 13

• a translation of 13 units to the right

Tags

CCSS.HSF.BF.B.3

What transformation occurred on the following function?  $f\left(x\right)=-2\ln\left(x-3\right)$ 

Check ALL that applies.

• Reflection

• Vertical Stretch

• Vertical Compression

• Horizontal Translation 3 units to the right

• Horizontal Translation 3 units to the left

The graph of which function  $g\left(x\right)$  is a translation 5 units down from the graph of  $f\left(x\right)=\ln\left(x\right)$  ?

•  $g\left(x\right)=\ln\left(x\right)-5$  

•  $g\left(x\right)=\frac{1}{5}x$  

•  $g\left(x\right)=\ln\left(x-5\right)$  

•  $g\left(x\right)=\ln\left(x+5\right)$  

Tags

CCSS.HSF.BF.B.3

The function shown in the graph is a translation of the parent function  $y=\ln\left(x\right)$  .  What is the function?

 

•  $y=5\log_ex$  

•  $y=\log_e\left(x-5\right)$  

•  $y=\log_e\left(x-6\right)$  

•  $y=\log_ex-6$  

Tags

CCSS.HSF-IF.C.7E