Test on Logarithms and Exponential Functions

What is the Domain of the function:
 $f\left(x\right)=-\log_3\left(x+3\right)$  

•  $\left(-\infty,\infty\right)$  

•  $\left(3,\infty\right)$  

•  $\left(-3,\infty\right)$  

•  $\left(-2,\infty\right)$  

What is the range of the function:
 $f\left(x\right)=-\log_3\left(x+3\right)$  

•  $\left(-\infty,\infty\right)$  

•  $\left(3,\infty\right)$  

•  $\left(-3,\infty\right)$  

•  $\left(-2,\infty\right)$  

Which answer choice is correct about the function:
 $f\left(x\right)=-\log_3\left(x+3\right)$  

• It has a vertical asymptote at  $x=-3$  

• It has a vertical asymptote at  $x=-2$  

• It has a horizontal asymptote at  $y=-3$  

• It has no asymptotes of any kind.

What is the y-intercept of the function:
 $f\left(x\right)=-\log_3\left(x+3\right)$  

•  $\left(0,-1\right)$  

•  $\left(-2,0\right)$  

• This function has no y-intercept

What is the x-intercept of this function:
 $f\left(x\right)=-\log_3\left(x+3\right)$  
 

•  $\left(0-1\right)$  

•  $\left(-2,0\right)$  

• This function has no x-intercept.

 $f\left(x\right)=-\log_3\left(x+3\right)$  

What is the end behavior for this function:

• as  $x$  approaches  $\infty$  ,  $y$   approaches  $\infty$  
  as $x$  approaches  $-\infty$  ,  $y$   approaches  $\infty$  

• as  $x$  approaches  $\infty$  ,  $y$   approaches  $-\infty$  
  as $x$  approaches  $-3$  ,  $y$   approaches  $\infty$  

• as  $x$  approaches  $\infty$  ,  $y$   approaches  $\infty$  
  as $x$  approaches  $-3$  ,  $y$   approaches  $-\infty$  

• as  $x$  approaches  $\infty$  ,  $y$   approaches  $-\infty$  
  as $x$  approaches  $-\infty$  ,  $y$   approaches  $-\infty$  

 $f\left(x\right)=-\log_3\left(x+3\right)$  

Is the function increasing or decreasing?

• Increasing

• Decreasing

Select the TWO transformations that apply to this function:
 $f\left(x\right)=-\log_3\left(x+3\right)$  

• Left 3

• Right 3

• Reflects over the x-axis

• Reflects over the y-axis

What is the Domain of the function:
 $f\left(x\right)=2^{\left(x+3\right)}-1$  

•  $\left(-\infty,\infty\right)$  

•  $\left(-1,\infty\right)$  

•  $\left(-3,\infty\right)$  

•  $\left(0,\infty\right)$  

What is the range of the function:
 $f\left(x\right)=2^{\left(x+3\right)}-1$  

•  $\left(-\infty,\infty\right)$  

•  $\left(-1,\infty\right)$  

•  $\left(-3,\infty\right)$  

•  $\left(0,\infty\right)$