HW: Graphing Logarithmic Functions

Which of the following is true about the general form of a logarithmic function,

 $f\left(x\right)=a\log_b\left(x-h\right)+k$  ? Select ALL that apply

• The horizontal asymptote is  $y=k$  

• The vertical asymptote is  $x=h$  

•  $h$  is the horizontal shift

•  $k$  is the vertical shift

•  $a$  reflects the graph over the x-axis if it's negative

What is the vertical asymptote for the graph of

 $f\left(x\right)=\log_4x$  ?

•  $y=0$  

•  $y=4$  

•  $x=0$  

•  $x=4$  

Describe the end behavior of the graph of

 $f\left(x\right)=\log_4x$  

• As  $x\rightarrow\infty$  ,  $y\rightarrow\infty$  

• As  $x\rightarrow\infty$  ,  $y\rightarrow-\infty$  

• As  $x\rightarrow0^+$  ,  $y\rightarrow\infty$  

• As  $x\rightarrow0^+$  ,  $y\rightarrow-\infty$  

Describe the transformation on

 $g\left(x\right)=\log_2\left(x-3\right)$  

• The graph has been shifted 3 units up

• The graph has been shifted 3 units to the right

• The graph has been shifted 2 units right

• The graph has been shifted 3 units left

What is the domain for

 $g\left(x\right)=\log_2\left(x-3\right)$  ?

• All real numbers

•  $\left(3,\infty\right)$  

•  $\left(0,\infty\right)$  

•  $\left(-\infty,3\right)$  

Describe the transformation for

 $h\left(x\right)=-\log_3\left(x+1\right)$ . Select ALL that apply.

•  $h$  has been reflected over the x-axis

•  $h$  has shifted 3 units to the left

•  $h$  has shifted 1 unit to the left

•  $h$  has reflected over the y-axis

Describe the end behavior for

 $h\left(x\right)=-\log_3\left(x+1\right)$  . Select ALL that apply.

• As  $x\rightarrow-1^-$  ,  $y\rightarrow-\infty$  

• As  $x\rightarrow\infty$  ,  $y\rightarrow\infty$  

• As  $x\rightarrow-1^+$  ,  $y\rightarrow\infty$  

• As  $x\rightarrow\infty$  ,  $y\rightarrow-\infty$  

Describe the transformation(s) for 

 $k\left(x\right)=\log_{10}\left(x-6\right)-4$  .

• k has been shifted 6 units right and 4 units down

• k has been shifted 6 units right and 4 units up

• k has been shifted 6 units left and 4 units down

• k has been shifted 6 units left and 4 units up

What is the equation for the graph?

• $y=\log_4\left(x+1\right)+2$

• $y=\log_4\left(x+2\right)+1$

• $y=\log_4\left(x-1\right)+2$

• $y=\log_4\left(x-2\right)+1$